diff --git a/src/sage/features/four_ti_2.py b/src/sage/features/four_ti_2.py
index bdc6399b82e..2889ef24d25 100644
--- a/src/sage/features/four_ti_2.py
+++ b/src/sage/features/four_ti_2.py
@@ -1,6 +1,8 @@
 from sage.env import SAGE_ENV
 
-from sage.features import Executable
+from . import Executable
+from .join_feature import JoinFeature
+
 
 class FourTi2Executable(Executable):
     r"""
@@ -11,3 +13,21 @@ def __init__(self, name):
                             name="4ti2-" + name,
                             executable=SAGE_ENV.get("FOURTITWO_" + name.upper(), None) or name,
                             spkg="4ti2")
+
+
+class FourTi2(JoinFeature):
+    r"""
+    A :class:`sage.features.Feature` describing the presence of the ``4ti2`` executables.
+
+    EXAMPLES::
+
+        sage: from sage.features.four_ti_2 import FourTi2
+        sage: FourTi2().is_present()  # optional - 4ti2
+        FeatureTestResult('4ti2', True)
+    """
+    def __init__(self):
+        JoinFeature.__init__(self, '4ti2',
+                             [FourTi2Executable(x)
+                              # same list is tested in build/pkgs/4ti2/spkg-configure.m4
+                              for x in ('hilbert', 'markov', 'graver', 'zsolve', 'qsolve',
+                                        'rays', 'ppi', 'circuits', 'groebner')])
diff --git a/src/sage/features/join_feature.py b/src/sage/features/join_feature.py
new file mode 100644
index 00000000000..f011b40a7f6
--- /dev/null
+++ b/src/sage/features/join_feature.py
@@ -0,0 +1,82 @@
+r"""
+Join features
+"""
+
+from . import Feature, FeatureTestResult
+
+
+class JoinFeature(Feature):
+    r"""
+    Join of several :class:`sage.features.Feature` instances.
+
+    EXAMPLES::
+
+        sage: from sage.features import Executable
+        sage: from sage.features.join_feature import JoinFeature
+        sage: F = JoinFeature("shell-boolean",
+        ....:                 (Executable('shell-true', 'true'),
+        ....:                  Executable('shell-false', 'false')))
+        sage: F.is_present()
+        FeatureTestResult('shell-boolean', True)
+        sage: F = JoinFeature("asdfghjkl",
+        ....:                 (Executable('shell-true', 'true'),
+        ....:                  Executable('xxyyyy', 'xxyyyy-does-not-exist')))
+        sage: F.is_present()
+        FeatureTestResult('xxyyyy', False)
+    """
+    def __init__(self, name, features, spkg=None, url=None):
+        """
+        TESTS:
+
+        The empty join feature is present::
+
+            sage: from sage.features.join_feature import JoinFeature
+            sage: JoinFeature("empty", ()).is_present()
+            FeatureTestResult('empty', True)
+        """
+        if spkg is None:
+            spkgs = set(f.spkg for f in features if f.spkg)
+            if len(spkgs) > 1:
+                raise ValueError('given features have more than one spkg; provide spkg argument')
+            elif len(spkgs) == 1:
+                spkg = next(iter(spkgs))
+        if url is None:
+            urls = set(f.url for f in features if f.url)
+            if len(urls) > 1:
+                raise ValueError('given features have more than one url; provide url argument')
+            elif len(urls) == 1:
+                url = next(iter(urls))
+        super().__init__(name, spkg=spkg, url=url)
+        self._features = features
+
+    def _is_present(self):
+        r"""
+        Test for the presence of the join feature.
+
+        EXAMPLES::
+
+            sage: from sage.features.latte import Latte
+            sage: Latte()._is_present()  # optional - latte_int
+            FeatureTestResult('LattE', True)
+        """
+        for f in self._features:
+            test = f._is_present()
+            if not test:
+                return test
+        return FeatureTestResult(self, True)
+
+    def is_functional(self):
+        r"""
+        Test whether the join feature is functional.
+
+        EXAMPLES::
+
+            sage: from sage.features.latte import Latte
+            sage: Latte().is_functional()  # optional - latte_int
+            FeatureTestResult('LattE', True)
+        """
+        for f in self._features:
+            test = f.is_functional()
+            if not test:
+                return test
+        return FeatureTestResult(self, True)
diff --git a/src/sage/features/latte.py b/src/sage/features/latte.py
index 5462331177d..6abc450281c 100644
--- a/src/sage/features/latte.py
+++ b/src/sage/features/latte.py
@@ -3,6 +3,8 @@
 Check for LattE
 """
 from . import Executable, Feature, FeatureTestResult
+from .join_feature import JoinFeature
+
 
 LATTE_URL = "https://www.math.ucdavis.edu/~latte/software.php"
 
@@ -27,7 +29,7 @@ def __init__(self):
                             url=LATTE_URL)
 
 
-class Latte(Feature):
+class Latte(JoinFeature):
     r"""
     A :class:`sage.features.Feature` describing the presence of the ``LattE``
     binaries which comes as a part of ``latte_int``.
@@ -46,39 +48,5 @@ def __init__(self):
             sage: isinstance(Latte(), Latte)
             True
         """
-        Feature.__init__(self, "LattE")
-
-    def _is_present(self):
-        r"""
-        Test for the presence of LattE binaries.
-
-        EXAMPLES::
-
-            sage: from sage.features.latte import Latte
-            sage: Latte()._is_present()  # optional - latte_int
-            FeatureTestResult('LattE', True)
-        """
-
-        test = (Latte_count()._is_present() and
-                Latte_integrate()._is_present())
-        if not test:
-            return test
-
-        return FeatureTestResult(self, True)
-
-    def is_functional(self):
-        r"""
-        Test whether count and integrate are functionals.
-
-        EXAMPLES::
-
-            sage: from sage.features.latte import Latte
-            sage: Latte().is_functional()  # optional - latte_int
-            FeatureTestResult('LattE', True)
-        """
-        test = (Latte_count().is_functional() and
-                Latte_integrate().is_functional())
-        if not test:
-            return test
-
-        return FeatureTestResult(self, True)
+        JoinFeature.__init__(self, "LattE",
+                             (Latte_count(), Latte_integrate()))