diff --git a/Help/variable/CMAKE_LANG_COMPILER_ARCHITECTURE_ID.rst b/Help/variable/CMAKE_LANG_COMPILER_ARCHITECTURE_ID.rst
index c6853e3654..0544e12631 100644
--- a/Help/variable/CMAKE_LANG_COMPILER_ARCHITECTURE_ID.rst
+++ b/Help/variable/CMAKE_LANG_COMPILER_ARCHITECTURE_ID.rst
@@ -6,8 +6,13 @@ CMAKE_<LANG>_COMPILER_ARCHITECTURE_ID
 :ref:`List <CMake Language Lists>` of identifiers indicating the
 target architecture(s) of the compiler for language ``<LANG>``.
 
-Typically the list has one entry unless :variable:`CMAKE_OSX_ARCHITECTURES`
-lists multiple architectures.
+Typically the list has one entry unless the compiler stores multiple
+architectures in each object file.  For example:
+
+* The build targets an Apple platform with
+  :variable:`CMAKE_OSX_ARCHITECTURES` listing multiple architectures.
+* The build targets Windows ARM64 with the MSVC ABI using Clang with
+  the ``-marm64x`` flag.
 
 Possible values for each platform are documented in the following sections.
 
diff --git a/Modules/CMakeDetermineCompilerId.cmake b/Modules/CMakeDetermineCompilerId.cmake
index a23e8e3460..52dafb9788 100644
--- a/Modules/CMakeDetermineCompilerId.cmake
+++ b/Modules/CMakeDetermineCompilerId.cmake
@@ -1139,7 +1139,7 @@ function(CMAKE_DETERMINE_COMPILER_ID_CHECK lang file)
         set(PLATFORM_ID "${CMAKE_MATCH_1}")
       endif()
       if("${info}" MATCHES "INFO:arch\\[([^]\"]*)\\]")
-        set(ARCHITECTURE_ID "${CMAKE_MATCH_1}")
+        list(APPEND ARCHITECTURE_ID "${CMAKE_MATCH_1}")
       endif()
       if("${info}" MATCHES "INFO:compiler_version\\[([^]\"]*)\\]")
         string(REGEX REPLACE "^0+([0-9]+)" "\\1" COMPILER_VERSION "${CMAKE_MATCH_1}")
@@ -1225,6 +1225,7 @@ function(CMAKE_DETERMINE_COMPILER_ID_CHECK lang file)
     if(COMPILER_ID AND NOT COMPILER_ID_TWICE)
       set(CMAKE_${lang}_COMPILER_ID "${COMPILER_ID}")
       set(CMAKE_${lang}_PLATFORM_ID "${PLATFORM_ID}")
+      list(SORT ARCHITECTURE_ID)
       set(CMAKE_${lang}_COMPILER_ARCHITECTURE_ID "${ARCHITECTURE_ID}")
       set(MSVC_${lang}_ARCHITECTURE_ID "${ARCHITECTURE_ID}")
       set(CMAKE_${lang}_COMPILER_VERSION "${COMPILER_VERSION}")