diff --git a/.gitlab/artifacts.yml b/.gitlab/artifacts.yml
index bd13646..bf8e8b6 100644
--- a/.gitlab/artifacts.yml
+++ b/.gitlab/artifacts.yml
@@ -71,6 +71,8 @@
 .cmake_release_artifacts:
     artifacts:
         expire_in: 5d
+        # Release artifacts are of interest even for failed jobs.
+        when: always
         paths:
             # Any packages made.
             - build/cmake-*-linux-x86_64.*
@@ -83,6 +85,8 @@
 .cmake_test_artifacts:
     artifacts:
         expire_in: 1d
+        # External testing can be useful even if test jobs fail.
+        when: always
         paths:
             # Take the install tree.
             - build/install/
diff --git a/.gitlab/os-macos.yml b/.gitlab/os-macos.yml
index 7fe6277..1ce96b3 100644
--- a/.gitlab/os-macos.yml
+++ b/.gitlab/os-macos.yml
@@ -7,7 +7,7 @@
         GIT_CLONE_PATH: "$CI_BUILDS_DIR/cmake ci ext/$CI_CONCURRENT_ID"
         # TODO: Factor this out so that each job selects the Xcode version to
         # use so that different versions can be tested in a single pipeline.
-        DEVELOPER_DIR: "/Applications/Xcode-12.3.app/Contents/Developer"
+        DEVELOPER_DIR: "/Applications/Xcode-12.4.app/Contents/Developer"
         # Avoid conflicting with other projects running on the same machine.
         SCCACHE_SERVER_PORT: 4227
 
@@ -70,6 +70,7 @@
     variables:
         CMAKE_CONFIGURATION: macos_x86_64_xcode
         CMAKE_GENERATOR: Xcode
+        CMAKE_CI_NIGHTLY_IGNORE_DEPS: "true"
 
 .macos_arm64_xcode:
     extends: .macos
@@ -77,6 +78,7 @@
     variables:
         CMAKE_CONFIGURATION: macos_arm64_xcode
         CMAKE_GENERATOR: Xcode
+        CMAKE_CI_NIGHTLY_IGNORE_DEPS: "true"
 
 ## Tags
 
@@ -85,7 +87,7 @@
         - cmake # Since this is a bare runner, pin to a project.
         - macos
         - shell
-        - xcode-12.3
+        - xcode-12.4
         - nonconcurrent
 
 .macos_x86_64_builder_tags_package:
@@ -93,7 +95,7 @@
         - cmake # Since this is a bare runner, pin to a project.
         - macos
         - shell
-        - xcode-12.3
+        - xcode-12.4
         - nonconcurrent
         - finder
 
@@ -102,7 +104,7 @@
         - cmake # Since this is a bare runner, pin to a project.
         - macos
         - shell
-        - xcode-12.3
+        - xcode-12.4
         - concurrent
 
 .macos_arm64_builder_tags:
@@ -110,7 +112,7 @@
         - cmake # Since this is a bare runner, pin to a project.
         - macos-arm64
         - shell
-        - xcode-12.3
+        - xcode-12.4
         - nonconcurrent
 
 .macos_arm64_builder_ext_tags:
@@ -118,7 +120,7 @@
         - cmake # Since this is a bare runner, pin to a project.
         - macos-arm64
         - shell
-        - xcode-12.3
+        - xcode-12.4
         - concurrent
 
 ## macOS-specific scripts
diff --git a/.gitlab/os-windows.yml b/.gitlab/os-windows.yml
index 1fff2bb..3e9634d 100644
--- a/.gitlab/os-windows.yml
+++ b/.gitlab/os-windows.yml
@@ -50,6 +50,7 @@
         CMAKE_GENERATOR: "Visual Studio 16 2019"
         CMAKE_GENERATOR_PLATFORM: "x64"
         CMAKE_GENERATOR_TOOLSET: "v142,version=14.28"
+        CMAKE_CI_NIGHTLY_IGNORE_DEPS: "true"
 
 ## Tags
 
diff --git a/.gitlab/rules.yml b/.gitlab/rules.yml
index e8c527d..b3e5342 100644
--- a/.gitlab/rules.yml
+++ b/.gitlab/rules.yml
@@ -38,6 +38,8 @@
     rules:
         - if: '$CMAKE_CI_PACKAGE == "true"'
           when: never
+        - if: '($CMAKE_CI_NIGHTLY == "true" && $CMAKE_CI_NIGHTLY_IGNORE_DEPS == "true")'
+          when: always
         - if: '$CMAKE_CI_NIGHTLY == "true"'
           when: on_success
         - if: '($CMAKE_CI_NO_MR == "true" && $CI_MERGE_REQUEST_ID)'
diff --git a/Help/guide/importing-exporting/MathFunctionsComponents/Addition/CMakeLists.txt b/Help/guide/importing-exporting/MathFunctionsComponents/Addition/CMakeLists.txt
index e3cf711..17ad952 100644
--- a/Help/guide/importing-exporting/MathFunctionsComponents/Addition/CMakeLists.txt
+++ b/Help/guide/importing-exporting/MathFunctionsComponents/Addition/CMakeLists.txt
@@ -26,5 +26,5 @@
 install(EXPORT AdditionTargets
         FILE MathFunctionsAdditionTargets.cmake
         NAMESPACE MathFunctions::
-        DESTINATION lib/cmake
+        DESTINATION lib/cmake/MathFunctions
 )
diff --git a/Help/guide/importing-exporting/MathFunctionsComponents/CMakeLists.txt b/Help/guide/importing-exporting/MathFunctionsComponents/CMakeLists.txt
index 4e3496d..fd95e28 100644
--- a/Help/guide/importing-exporting/MathFunctionsComponents/CMakeLists.txt
+++ b/Help/guide/importing-exporting/MathFunctionsComponents/CMakeLists.txt
@@ -24,7 +24,7 @@
 # create config file
 configure_package_config_file(${CMAKE_CURRENT_SOURCE_DIR}/Config.cmake.in
   "${CMAKE_CURRENT_BINARY_DIR}/MathFunctionsConfig.cmake"
-  INSTALL_DESTINATION lib/cmake
+  INSTALL_DESTINATION lib/cmake/MathFunctions
   NO_CHECK_REQUIRED_COMPONENTS_MACRO
 )
 
@@ -32,5 +32,5 @@
 install(FILES
           "${CMAKE_CURRENT_BINARY_DIR}/MathFunctionsConfig.cmake"
           "${CMAKE_CURRENT_BINARY_DIR}/MathFunctionsConfigVersion.cmake"
-        DESTINATION lib/cmake
+        DESTINATION lib/cmake/MathFunctions
 )
diff --git a/Help/guide/importing-exporting/MathFunctionsComponents/SquareRoot/CMakeLists.txt b/Help/guide/importing-exporting/MathFunctionsComponents/SquareRoot/CMakeLists.txt
index ffa1e3d..be5ae65 100644
--- a/Help/guide/importing-exporting/MathFunctionsComponents/SquareRoot/CMakeLists.txt
+++ b/Help/guide/importing-exporting/MathFunctionsComponents/SquareRoot/CMakeLists.txt
@@ -26,5 +26,5 @@
 install(EXPORT SquareRootTargets
         FILE MathFunctionsSquareRootTargets.cmake
         NAMESPACE MathFunctions::
-        DESTINATION lib/cmake
+        DESTINATION lib/cmake/MathFunctions
 )
diff --git a/Modules/CMakeDetermineCompilerId.cmake b/Modules/CMakeDetermineCompilerId.cmake
index 1be570e..1595cfd 100644
--- a/Modules/CMakeDetermineCompilerId.cmake
+++ b/Modules/CMakeDetermineCompilerId.cmake
@@ -1,6 +1,17 @@
 # Distributed under the OSI-approved BSD 3-Clause License.  See accompanying
 # file Copyright.txt or https://cmake.org/licensing for details.
 
+macro(__determine_compiler_id_test testflags_in userflags)
+  separate_arguments(testflags UNIX_COMMAND "${testflags_in}")
+  CMAKE_DETERMINE_COMPILER_ID_BUILD("${lang}" "${testflags}" "${userflags}" "${src}")
+  CMAKE_DETERMINE_COMPILER_ID_MATCH_VENDOR("${lang}" "${COMPILER_${lang}_PRODUCED_OUTPUT}")
+
+  if(NOT CMAKE_${lang}_COMPILER_ID)
+    foreach(file ${COMPILER_${lang}_PRODUCED_FILES})
+      CMAKE_DETERMINE_COMPILER_ID_CHECK("${lang}" "${CMAKE_${lang}_COMPILER_ID_DIR}/${file}" "${src}")
+    endforeach()
+  endif()
+endmacro()
 
 # Function to compile a source file to identify the compiler.  This is
 # used internally by CMake and should not be included by user code.
@@ -24,29 +35,36 @@
   # Compute the directory in which to run the test.
   set(CMAKE_${lang}_COMPILER_ID_DIR ${CMAKE_PLATFORM_INFO_DIR}/CompilerId${lang})
 
-  # Try building with no extra flags and then try each set
-  # of helper flags.  Stop when the compiler is identified.
-  foreach(userflags "${CMAKE_${lang}_COMPILER_ID_FLAGS_LIST}" "")
-    foreach(testflags ${CMAKE_${lang}_COMPILER_ID_TEST_FLAGS_FIRST}
-                      ""
-                      ${CMAKE_${lang}_COMPILER_ID_TEST_FLAGS})
-      separate_arguments(testflags UNIX_COMMAND "${testflags}")
-      CMAKE_DETERMINE_COMPILER_ID_BUILD("${lang}" "${testflags}" "${userflags}" "${src}")
-      CMAKE_DETERMINE_COMPILER_ID_MATCH_VENDOR("${lang}" "${COMPILER_${lang}_PRODUCED_OUTPUT}")
+  # If we REQUIRE_SUCCESS, i.e. TEST_FLAGS_FIRST has the correct flags, we still need to
+  # try two combinations: with COMPILER_ID_FLAGS (from user) and without (see issue #21869).
+  if(CMAKE_${lang}_COMPILER_ID_REQUIRE_SUCCESS)
+    # If there COMPILER_ID_FLAGS is empty we can error for the first invocation.
+    if("${CMAKE_${lang}_COMPILER_ID_FLAGS_LIST}" STREQUAL "")
+      set(__compiler_id_require_success TRUE)
+    endif()
+
+    foreach(userflags "${CMAKE_${lang}_COMPILER_ID_FLAGS_LIST}" "")
+      __determine_compiler_id_test("${CMAKE_${lang}_COMPILER_ID_TEST_FLAGS_FIRST}" "${userflags}")
       if(CMAKE_${lang}_COMPILER_ID)
         break()
       endif()
-      foreach(file ${COMPILER_${lang}_PRODUCED_FILES})
-        CMAKE_DETERMINE_COMPILER_ID_CHECK("${lang}" "${CMAKE_${lang}_COMPILER_ID_DIR}/${file}" "${src}")
+      set(__compiler_id_require_success TRUE)
+    endforeach()
+  else()
+    # Try building with no extra flags and then try each set
+    # of helper flags.  Stop when the compiler is identified.
+    foreach(userflags "${CMAKE_${lang}_COMPILER_ID_FLAGS_LIST}" "")
+      foreach(testflags ${CMAKE_${lang}_COMPILER_ID_TEST_FLAGS_FIRST} "" ${CMAKE_${lang}_COMPILER_ID_TEST_FLAGS})
+        __determine_compiler_id_test("${testflags}" "${userflags}")
+        if(CMAKE_${lang}_COMPILER_ID)
+          break()
+        endif()
       endforeach()
       if(CMAKE_${lang}_COMPILER_ID)
         break()
       endif()
     endforeach()
-    if(CMAKE_${lang}_COMPILER_ID)
-      break()
-    endif()
-  endforeach()
+  endif()
 
   # Check if compiler id detection gave us the compiler tool.
   if(CMAKE_${lang}_COMPILER_ID_TOOL)
@@ -653,7 +671,7 @@
 
     # Some languages may know the correct/desired set of flags and want to fail right away if they don't work.
     # This is currently only used by CUDA.
-    if(CMAKE_${lang}_COMPILER_ID_REQUIRE_SUCCESS)
+    if(__compiler_id_require_success)
       message(FATAL_ERROR "${MSG}")
     endif()
 
diff --git a/Modules/FindOpenGL.cmake b/Modules/FindOpenGL.cmake
index 4766102..d6d1c00 100644
--- a/Modules/FindOpenGL.cmake
+++ b/Modules/FindOpenGL.cmake
@@ -465,7 +465,7 @@
 
   # ::GLX is a GLVND library, and thus Linux-only: we don't bother checking
   # for a framework version of this library.
-  if(OpenGL_GLX_FOUND AND NOT TARGET OpenGL::GLX)
+  if(OpenGL_GLX_FOUND AND NOT TARGET OpenGL::GLX AND TARGET OpenGL::OpenGL)
     if(IS_ABSOLUTE "${OPENGL_glx_LIBRARY}")
       add_library(OpenGL::GLX UNKNOWN IMPORTED)
       set_target_properties(OpenGL::GLX PROPERTIES IMPORTED_LOCATION