diff --git a/faces/bin/run-tck.sh b/faces/bin/run-tck.sh
index e9aaa99..6a3d4ea 100755
--- a/faces/bin/run-tck.sh
+++ b/faces/bin/run-tck.sh
@@ -115,7 +115,7 @@ if [ ! -d "${WORK_DIR}" ]; then
     mkdir -p "${WORK_DIR}"
 fi
 if [ -z "${TCK_VERSION}" ]; then
-    TCK_VERSION="4.0.2"
+    TCK_VERSION="4.0.3"
 fi
 TCK_ZIP="${WORK_DIR}/jakarta-faces-tck-${TCK_VERSION}.zip"
 TCK_URL=https://download.eclipse.org/jakartaee/faces/4.0/jakarta-faces-tck-${TCK_VERSION}.zip
@@ -206,10 +206,19 @@ if [ ${skipNewTck} == true ]; then
 else
     echo "Executing NEW Jakarta Faces TCK."
     pushd $TCK_ROOT
-    safeRun mvn ${MVN_ARGS} clean install -pl '!old-tck,!old-tck/build,!old-tck/run' \
+    # Run the bulk of the TCK with a excludes files to possibly exclude tests classes/methods with accepted challenges
+    safeRun mvn ${MVN_ARGS} clean install -pl '!old-tck,!old-tck/build,!old-tck/run,!faces-signaturetest' \
         -P 'new-wildfly,wildfly-ci-managed,!glassfish-ci-managed' \
-        -Dwildfly.dir="${NEW_WILDFLY}" -fae
+        -Dwildfly.dir="${NEW_WILDFLY}" \
+        -Dnewtck.exclusions="${BASE_DIR}/wildfly-mods/newtck-exclusions.txt" \
+        -Dse21.newtck.exclusions="${BASE_DIR}/wildfly-mods/se21-newtck-exclusions.txt" \
+        -fae
     newTckStatus=${status}
+    # Don't use an excludesFile for the signature tests; it doesn't allow excluded methods
+    safeRun mvn ${MVN_ARGS} clean install -pl 'faces-signaturetest' \
+        -P 'new-wildfly,wildfly-ci-managed,!glassfish-ci-managed' \
+        -Dwildfly.dir="${NEW_WILDFLY}" -fae
+    newTckStatus &&= ${status}
     # Run the reporting
     safeRun curl -Ls https://sh.jbang.dev | bash -s - run "${SCRIPT_DIR}/parsesurefire.java" --batch --format "Tests run: %p, Failures: %f, Errors: %e" "${TCK_ROOT}"
     if [ ${status} -ne 0 ]; then
diff --git a/faces/wildfly-mods/global-excludes-profile.xml b/faces/wildfly-mods/global-excludes-profile.xml
new file mode 100644
index 0000000..6a4cc67
--- /dev/null
+++ b/faces/wildfly-mods/global-excludes-profile.xml
@@ -0,0 +1,21 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+        <profile xmlns="http://maven.apache.org/POM/4.0.0">
+		    <!-- Exclude accepted TCK challenges that are relevant in all contexts. -->
+            <id>global-tck-challenges</id>
+            <activation>
+				<property><name>newtck.exclusions</name></property>
+            </activation>
+
+            <build>
+            	<plugins>
+            	    <plugin>
+            	        <groupId>org.apache.maven.plugins</groupId>
+            	        <artifactId>maven-failsafe-plugin</artifactId>
+            	        <configuration>
+            	            <excludesFile>${newtck.exclusions}</excludesFile>
+            	        </configuration>
+            	    </plugin>
+            	</plugins>
+            </build>
+        </profile>
\ No newline at end of file
diff --git a/faces/wildfly-mods/newtck-exclusions.txt b/faces/wildfly-mods/newtck-exclusions.txt
new file mode 100644
index 0000000..1baf422
--- /dev/null
+++ b/faces/wildfly-mods/newtck-exclusions.txt
@@ -0,0 +1,4 @@
+# Add entries for accepted challenges that are applicable in all contexts. 
+# Add a comment linking to the challenge, followed by ant globs pointing to the test class. 
+# To exclude a single method, append '#theMethodName' to the glob.
+#
diff --git a/faces/wildfly-mods/se21-excludes-profile.xml b/faces/wildfly-mods/se21-excludes-profile.xml
new file mode 100644
index 0000000..a79073a
--- /dev/null
+++ b/faces/wildfly-mods/se21-excludes-profile.xml
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+        <profile xmlns="http://maven.apache.org/POM/4.0.0">
+			<!-- Exclude accepted TCK challenges that are only relevant to SE 21 or later. -->
+            <id>se21-tck-challenges</id>
+            <activation>
+                <jdk>[21,)</jdk>
+				<property><name>se21.newtck.exclusions</name></property>
+            </activation>
+
+            <build>
+            	<plugins>
+            	    <plugin>
+            	        <groupId>org.apache.maven.plugins</groupId>
+            	        <artifactId>maven-failsafe-plugin</artifactId>
+            	        <configuration>
+            	            <excludesFile>${se21.newtck.exclusions}</excludesFile>
+            	        </configuration>
+            	    </plugin>
+            	</plugins>
+            </build>
+        </profile>
diff --git a/faces/wildfly-mods/se21-newtck-exclusions.txt b/faces/wildfly-mods/se21-newtck-exclusions.txt
new file mode 100644
index 0000000..7f84c71
--- /dev/null
+++ b/faces/wildfly-mods/se21-newtck-exclusions.txt
@@ -0,0 +1,8 @@
+# Add entries for accepted challenges that are specific to SE 21 or later. 
+# Add a comment linking to the challenge, followed by ant globs pointing to the test class. 
+# To exclude a single method, append '#theMethodName' to the glob.
+#
+# Challenge https://github.com/jakartaee/faces/issues/1935
+**/ee/jakarta/tck/faces/test/javaee8/converter/Issue4070IT#testJavaTimeTypes
+**/ee/jakarta/tck/faces/test/javaee8/converter/Issue4087IT#testJavaTimeTypes
+**/ee/jakarta/tck/faces/test/javaee8/converter/Issue4110IT#testJavaTimeTypes
\ No newline at end of file
diff --git a/faces/wildfly-mods/transform.xslt b/faces/wildfly-mods/transform.xslt
index cef0e30..606ea76 100644
--- a/faces/wildfly-mods/transform.xslt
+++ b/faces/wildfly-mods/transform.xslt
@@ -13,6 +13,8 @@
                          //*[local-name()='profiles']">
         <xsl:copy>
             <xsl:apply-templates select="document('profile.xml')/*"/>
+            <xsl:apply-templates select="document('global-excludes-profile.xml')/*"/>
+            <xsl:apply-templates select="document('se21-excludes-profile.xml')/*"/>
             <xsl:apply-templates select="node()|@*"/>
         </xsl:copy>
     </xsl:template>