diff --git a/Manifest.toml b/Manifest.toml
new file mode 100644
index 0000000..76e4570
--- /dev/null
+++ b/Manifest.toml
@@ -0,0 +1,145 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[BenchmarkTools]]
+deps = ["JSON", "Printf", "Statistics"]
+git-tree-sha1 = "90b73db83791c5f83155016dd1cc1f684d4e1361"
+uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+version = "0.4.3"
+
+[[BinaryProvider]]
+deps = ["Libdl", "SHA"]
+git-tree-sha1 = "5b08ed6036d9d3f0ee6369410b830f8873d4024c"
+uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
+version = "0.5.8"
+
+[[CodecBzip2]]
+deps = ["BinaryProvider", "Libdl", "TranscodingStreams"]
+git-tree-sha1 = "5db086e510c11b4c87d05067627eadb2dc079995"
+uuid = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd"
+version = "0.6.0"
+
+[[CodecZlib]]
+deps = ["BinaryProvider", "Libdl", "TranscodingStreams"]
+git-tree-sha1 = "05916673a2627dd91b4969ff8ba6941bc85a960e"
+uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
+version = "0.6.0"
+
+[[Dates]]
+deps = ["Printf"]
+uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
+
+[[Distributed]]
+deps = ["Random", "Serialization", "Sockets"]
+uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+
+[[HTTP]]
+deps = ["Base64", "Dates", "IniFile", "MbedTLS", "Sockets"]
+git-tree-sha1 = "5c49dab19938b119fe204fd7d7e8e174f4e9c68b"
+uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
+version = "0.8.8"
+
+[[IniFile]]
+deps = ["Test"]
+git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
+uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
+version = "0.5.0"
+
+[[InteractiveUtils]]
+deps = ["Markdown"]
+uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+
+[[JSON]]
+deps = ["Dates", "Mmap", "Parsers", "Unicode"]
+git-tree-sha1 = "b34d7cef7b337321e97d22242c3c2b91f476748e"
+uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+version = "0.21.0"
+
+[[JSONSchema]]
+deps = ["HTTP", "JSON", "Test"]
+git-tree-sha1 = "6f80c4ea9ccf648766380b28b63efd1050dee940"
+uuid = "7d188eb4-7ad8-530c-ae41-71a32a6d4692"
+version = "0.1.1"
+
+[[Libdl]]
+uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
+
+[[LinearAlgebra]]
+deps = ["Libdl"]
+uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
+[[Logging]]
+uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
+
+[[Markdown]]
+deps = ["Base64"]
+uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
+
+[[MathOptInterface]]
+deps = ["BenchmarkTools", "LinearAlgebra", "OrderedCollections", "SparseArrays", "Test", "Unicode"]
+git-tree-sha1 = "2cbf5d6dde94a85dd28ef702ef637079dc587728"
+repo-rev = "od/multi-objective"
+repo-url = "https://github.com/JuliaOpt/MathOptInterface.jl.git"
+uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
+version = "0.9.7"
+
+[[MbedTLS]]
+deps = ["BinaryProvider", "Dates", "Distributed", "Libdl", "Random", "Sockets", "Test"]
+git-tree-sha1 = "2d94286a9c2f52c63a16146bb86fd6cdfbf677c6"
+uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
+version = "0.6.8"
+
+[[Mmap]]
+uuid = "a63ad114-7e13-5084-954f-fe012c677804"
+
+[[OrderedCollections]]
+deps = ["Random", "Serialization", "Test"]
+git-tree-sha1 = "c4c13474d23c60d20a67b217f1d7f22a40edf8f1"
+uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+version = "1.1.0"
+
+[[Parsers]]
+deps = ["Dates", "Test"]
+git-tree-sha1 = "0139ba59ce9bc680e2925aec5b7db79065d60556"
+uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
+version = "0.3.10"
+
+[[Printf]]
+deps = ["Unicode"]
+uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+
+[[Random]]
+deps = ["Serialization"]
+uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+
+[[SHA]]
+uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
+
+[[Serialization]]
+uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+
+[[Sockets]]
+uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
+
+[[SparseArrays]]
+deps = ["LinearAlgebra", "Random"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[Statistics]]
+deps = ["LinearAlgebra", "SparseArrays"]
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[Test]]
+deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
+uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[TranscodingStreams]]
+deps = ["Random", "Test"]
+git-tree-sha1 = "7c53c35547de1c5b9d46a4797cf6d8253807108c"
+uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
+version = "0.9.5"
+
+[[Unicode]]
+uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
diff --git a/Project.toml b/Project.toml
index 130b2ec..84c3769 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "MathOptFormat"
 uuid = "f4570300-c277-12e8-125c-4912f86ce65d"
 authors = ["Oscar Dowson <oscar.dowson@northwestern.edu"]
-version = "0.3"
+version = "0.3.0"
 
 [deps]
 CodecBzip2 = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd"
diff --git a/src/CBF/CBF.jl b/src/CBF/CBF.jl
index ceb48dd..411c97c 100644
--- a/src/CBF/CBF.jl
+++ b/src/CBF/CBF.jl
@@ -29,6 +29,17 @@ function MOI.supports_constraint(
     return true
 end
 
+function MOI.supports(
+    ::InnerModel,
+    ::MOI.ObjectiveFunction{<:Union{
+        MOI.VectorOfVariables,
+        MOI.VectorAffineFunction{Float64},
+        MOI.VectorQuadraticFunction{Float64}
+    }}
+)
+    return false
+end
+
 struct Options end
 
 get_options(m::InnerModel) = get(m.ext, :CBF_OPTIONS, Options())
diff --git a/src/LP/LP.jl b/src/LP/LP.jl
index 45460bf..a5642e1 100644
--- a/src/LP/LP.jl
+++ b/src/LP/LP.jl
@@ -16,6 +16,18 @@ MOI.Utilities.@model(InnerModel,
     ()
 )
 
+function MOI.supports(
+    ::InnerModel,
+    ::MOI.ObjectiveFunction{<:Union{
+        MOI.ScalarQuadraticFunction{Float64},
+        MOI.VectorOfVariables,
+        MOI.VectorAffineFunction{Float64},
+        MOI.VectorQuadraticFunction{Float64}
+    }}
+)
+    return false
+end
+
 struct Options
     maximum_length::Int
     warn::Bool
diff --git a/src/MPS/MPS.jl b/src/MPS/MPS.jl
index c84aa33..787790b 100644
--- a/src/MPS/MPS.jl
+++ b/src/MPS/MPS.jl
@@ -16,6 +16,16 @@ MOI.Utilities.@model(InnerModel,
     ()
 )
 
+function MOI.supports(
+    ::InnerModel,
+    ::MOI.ObjectiveFunction{<:Union{
+        MOI.ScalarQuadraticFunction,
+        MOI.VectorQuadraticFunction
+    }}
+)
+    return false
+end
+
 struct Options
     warn::Bool
 end
@@ -32,7 +42,7 @@ Keyword arguments are:
  - `warn::Bool=false`: print a warning when variables or constraints are renamed.
 """
 function Model(;
-        warn::Bool = false
+    warn::Bool = false
 )
     model = InnerModel{Float64}()
     model.ext[:MPS_OPTIONS] = Options(warn)
@@ -55,7 +65,10 @@ function MOI.write_to_file(model::InnerModel, io::IO)
     MathOptFormat.create_unique_names(
         model;
         warn = options.warn,
-        replacements = Function[s -> replace(s, ' ' => '_')]
+        replacements = Function[
+            s -> replace(s, ' ' => '_')
+            s -> replace(s, r"^OBJ" => "_OBJ")
+        ]
     )
     write_model_name(io, model)
     write_rows(io, model)
@@ -90,7 +103,15 @@ const LINEAR_CONSTRAINTS = (
 )
 
 function write_rows(io::IO, model::InnerModel)
-    println(io, "ROWS\n N  OBJ")
+    obj_type = MOI.get(model, MOI.ObjectiveFunctionType())
+    obj_func = MOI.get(model, MOI.ObjectiveFunction{obj_type}())
+    if MOI.output_dimension(obj_func) == 1
+        println(io, "ROWS\n N  OBJ")
+    else
+        for i = 1:MOI.output_dimension(obj_func)
+            println(io, "ROWS\n N  OBJ$(i)")
+        end
+    end
     for (set_type, sense_char) in LINEAR_CONSTRAINTS
         for index in MOI.get(model, MOI.ListOfConstraintIndices{
                                         MOI.ScalarAffineFunction{Float64},
@@ -132,8 +153,12 @@ function add_coefficient(coefficients, variable_name, row_name, coefficient)
 end
 
 function extract_terms(
-        model::InnerModel, coefficients, row_name::String,
-        func::MOI.ScalarAffineFunction, discovered_columns::Set{String})
+    model::InnerModel,
+    coefficients,
+    row_name::String,
+    func::MOI.ScalarAffineFunction,
+    discovered_columns::Set{String}
+)
     for term in func.terms
         variable_name = MOI.get(model, MOI.VariableName(), term.variable_index)
         add_coefficient(coefficients, variable_name, row_name, term.coefficient)
@@ -143,14 +168,35 @@ function extract_terms(
 end
 
 function extract_terms(
-        model::InnerModel, coefficients, row_name::String, func::MOI.SingleVariable,
-        discovered_columns::Set{String})
+    model::InnerModel,
+    coefficients,
+    row_name::String,
+    func::MOI.SingleVariable,
+    discovered_columns::Set{String}
+)
     variable_name = MOI.get(model, MOI.VariableName(), func.variable)
     add_coefficient(coefficients, variable_name, row_name, 1.0)
     push!(discovered_columns, variable_name)
     return
 end
 
+function extract_terms(
+    model::InnerModel,
+    coefficients,
+    row_name::String,
+    func::MOI.VectorAffineFunction,
+    discovered_columns::Set{String}
+)
+    for v_term in func.terms
+        term = v_term.scalar_term
+        c_name = row_name * v_term.output_index
+        v_name = MOI.get(model, MOI.VariableName(), term.variable_index)
+        add_coefficient(coefficients, v_name, c_name, term.coefficient)
+        push!(discovered_columns, v_name)
+    end
+    return
+end
+
 function write_columns(io::IO, model::InnerModel)
     # Many MPS readers (e.g., CPLEX and GAMS) will error if a variable (column)
     # appears in the BOUNDS section but did not appear in the COLUMNS section.
@@ -163,13 +209,17 @@ function write_columns(io::IO, model::InnerModel)
     println(io, "COLUMNS")
     coefficients = Dict{String, Vector{Tuple{String, Float64}}}()
     for (set_type, sense_char) in LINEAR_CONSTRAINTS
-        for index in MOI.get(model, MOI.ListOfConstraintIndices{
-                                        MOI.ScalarAffineFunction{Float64},
-                                        set_type}())
+        for index in MOI.get(
+            model,
+            MOI.ListOfConstraintIndices{
+                MOI.ScalarAffineFunction{Float64}, set_type
+            }()
+        )
             row_name = MOI.get(model, MOI.ConstraintName(), index)
             func = MOI.get(model, MOI.ConstraintFunction(), index)
             extract_terms(
-                model, coefficients, row_name, func, discovered_columns)
+                model, coefficients, row_name, func, discovered_columns
+            )
         end
     end
     obj_func_type = MOI.get(model, MOI.ObjectiveFunctionType())
@@ -180,7 +230,7 @@ function write_columns(io::IO, model::InnerModel)
         # coefficients.
         for (v_name, terms) in coefficients
             for (idx, (row_name, coef)) in enumerate(terms)
-                if row_name == "OBJ"
+                if startswith(row_name, "OBJ")
                     terms[idx] = (row_name, -coef)
                 end
             end
@@ -459,12 +509,19 @@ end
 
 mutable struct TempMPSModel
     name::String
-    obj_name::String
+    obj_names::Vector{String}
     columns::Dict{String, TempColumn}
     rows::Dict{String, TempRow}
     intorg_flag::Bool  # A flag used to parse COLUMNS section.
-    TempMPSModel() = new("", "", Dict{String, TempColumn}(),
-        Dict{String, TempRow}(), false)
+    function TempMPSModel()
+        return new(
+            "",
+            String[],
+            Dict{String, TempColumn}(),
+            Dict{String, TempRow}(),
+            false
+        )
+    end
 end
 
 const HEADERS = ("ROWS", "COLUMNS", "RHS", "RANGES", "BOUNDS", "SOS", "ENDATA")
@@ -546,33 +603,45 @@ function copy_to(model::InnerModel, temp::TempMPSModel)
     end
     # Add linear constraints.
     for (c_name, row) in temp.rows
-        if c_name == temp.obj_name
-            # Set objective.
-            MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
-            obj_func = if length(row.terms) == 1 &&
-                    first(row.terms).second == 1.0
-                MOI.SingleVariable(variable_map[first(row.terms).first])
-            else
-                MOI.ScalarAffineFunction([
-                    MOI.ScalarAffineTerm(coef, variable_map[v_name])
-                        for (v_name, coef) in row.terms],
-                0.0)
-            end
-            MOI.set(model, MOI.ObjectiveFunction{typeof(obj_func)}(), obj_func)
+        if c_name in temp.obj_names
+            continue
+        end
+        constraint_function = MOI.ScalarAffineFunction([
+            MOI.ScalarAffineTerm(coef, variable_map[v_name])
+                for (v_name, coef) in row.terms],
+            0.0)
+        set = bounds_to_set(row.lower, row.upper)
+        if set !== nothing
+            c = MOI.add_constraint(model, constraint_function, set)
+            MOI.set(model, MOI.ConstraintName(), c, c_name)
         else
-            constraint_function = MOI.ScalarAffineFunction([
-                MOI.ScalarAffineTerm(coef, variable_map[v_name])
-                    for (v_name, coef) in row.terms],
-                0.0)
-            set = bounds_to_set(row.lower, row.upper)
-            if set !== nothing
-                c = MOI.add_constraint(model, constraint_function, set)
-                MOI.set(model, MOI.ConstraintName(), c, c_name)
-            else
-                error("Expected a non-empty set for $(c_name). Got row=$(row)")
+            error("Expected a non-empty set for $(c_name). Got row=$(row)")
+        end
+    end
+    # Set objective.
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+    obj_func = if length(temp.obj_names) == 1
+        row = temp.rows[first(temp.obj_names)]
+        MOI.ScalarAffineFunction(
+            [MOI.ScalarAffineTerm(coef, variable_map[v_name]) for (v_name, coef) in row.terms],
+            0.0
+        )
+    else
+        v_terms = MOI.VectorAffineTerm{Float64}[]
+        for (i, name) in enumerate(temp.obj_names)
+            row = temp.rows[name]
+            for (v_name, coef) in row.terms
+                push!(
+                    v_terms,
+                    MOI.VectorAffineTerm(
+                        i, MOI.ScalarAffineTerm(coef, variable_map[v_name])
+                    )
+                )
             end
         end
+        MOI.VectorAffineFunction(v_terms, zeros(length(temp.obj_names)))
     end
+    MOI.set(model, MOI.ObjectiveFunction{typeof(obj_func)}(), obj_func)
     return
 end
 
@@ -603,20 +672,14 @@ function parse_rows_line(data::TempMPSModel, items::Vector{String})
     sense, name = items
     if haskey(data.rows, name)
         error("Duplicate row encountered: $(line).")
-    elseif sense != "N" && sense != "L" && sense != "G" && sense != "E"
+    elseif !(sense in ("N", "L", "G", "E"))
         error("Invalid row sense: $(join(items, " "))")
     end
     row = TempRow()
     row.sense = sense
     if sense == "N"
-        if data.obj_name != ""
-            # Detected a duplicate objective. Skip it.
-            return name
-        end
-        data.obj_name = name
-    end
-    # Add some default bounds for the constraints.
-    if sense == "G"
+        push!(data.obj_names, name)
+    elseif sense == "G"
         row.lower = 0.0
     elseif sense == "L"
         row.upper = 0.0
@@ -635,7 +698,7 @@ end
 function parse_single_coefficient(data, row_name, column_name, value)
     row = get(data.rows, row_name, nothing)
     if row === nothing
-        error("ROW name $(row_name) not recognised. Is it in the ROWS field?")
+        error("Row name $(row_name) not recognised. Is it in the ROWS field?")
     end
     if haskey(row.terms, column_name)
         row.terms[column_name] += parse(Float64, value)
diff --git a/src/MathOptFormat.jl b/src/MathOptFormat.jl
index c8c8424..d6435c3 100644
--- a/src/MathOptFormat.jl
+++ b/src/MathOptFormat.jl
@@ -153,6 +153,7 @@ based on the extension (regardless of compression format).
     FORMAT_CBF,
     FORMAT_LP,
     FORMAT_MOF,
+    FORMAT_MOP,
     FORMAT_MPS,
     AUTOMATIC_FILE_FORMAT,
 )
@@ -162,6 +163,7 @@ const _FILE_FORMATS = Dict{FileFormat, Tuple{String, Any}}(
     FORMAT_CBF => (".cbf", CBF.Model),
     FORMAT_LP => (".lp", LP.Model),
     FORMAT_MOF => (".mof.json", MOF.Model),
+    FORMAT_MOP => (".mop", MPS.Model),
     FORMAT_MPS => (".mps", MPS.Model)
 )
 
diff --git a/test/MPS/MPS.jl b/test/MPS/MPS.jl
index ac7b377..20f1159 100644
--- a/test/MPS/MPS.jl
+++ b/test/MPS/MPS.jl
@@ -103,7 +103,7 @@ end
     model_2 = MPS.Model()
     MOIU.loadfromstring!(model_2, """
     variables: x, y, z
-    minobjective: x + y + z
+    minobjective: [x + y + z, x + 2 * y]
     con1: 1.0 * x in Interval(1.0, 5.0)
     con2: 1.0 * x in Interval(2.0, 6.0)
     con3: 1.0 * x in Interval(3.0, 7.0)