diff -u b/core/tests/Drupal/KernelTests/Core/Common/DrupalCheckIncompatibilityTest.php b/core/tests/Drupal/KernelTests/Core/Common/DrupalCheckIncompatibilityTest.php
--- b/core/tests/Drupal/KernelTests/Core/Common/DrupalCheckIncompatibilityTest.php
+++ b/core/tests/Drupal/KernelTests/Core/Common/DrupalCheckIncompatibilityTest.php
@@ -56,6 +56,15 @@
       ['drupal_migrate_ui(>8.x-0.1-alpha1)', '3.1.x-dev', NULL],
       // The situation for Big Pipe when it was included in core.
       ['big_pipe(>=8.x-1.0-rc1)', '8.x-2.0-alpha1', NULL],
+      // Just as BigPipe went into core with a major version number >1, so
+      // might other modules with even larger major version numbers. Check that
+      // once the module is no longer experimental and receives core's version
+      // number, that core's is larger.
+      ['experimental_module_test(>8.x-8.0)', '8.1.x-dev', NULL],
+      // However, check also that a contrib module can override a core module
+      // and specify a version number larger than core's. See
+      // https://www.drupal.org/node/2688369 for where this might be relevant.
+      ['some_contrib_module(>8.x-8.1)', '8.1.x-dev', ' (>8.x-8.1)'],
     ];
   }