diff --git a/EESSI-extend-2023.06-easybuild.eb b/EESSI-extend-2023.06-easybuild.eb
index 76e96766f9..b525ee462d 100644
--- a/EESSI-extend-2023.06-easybuild.eb
+++ b/EESSI-extend-2023.06-easybuild.eb
@@ -139,12 +139,17 @@ setenv ("EASYBUILD_SYSROOT", sysroot)
 setenv ("EASYBUILD_PREFIX", pathJoin(working_dir, "easybuild"))
 setenv ("EASYBUILD_INSTALLPATH", easybuild_installpath)
 setenv ("EASYBUILD_HOOKS", pathJoin(os.getenv("EESSI_PREFIX"), "init", "easybuild", "eb_hooks.py"))
-setenv ("EASYBUILD_UMASK", "002")
+
+-- Make sure to use the general umask that allows a global read
+setenv ("EASYBUILD_UMASK", "022")
+
+-- Allow this module to be loaded when running EasyBuild
+setenv ("EASYBUILD_ALLOW_LOADED_MODULES", "EasyBuild,EESSI-extend")
 
 -- Set all related environment variables if we have project or user installations (including extending MODULEPATH)
 if (user_modulepath ~= nil) then
   -- Use a more restrictive umask for this case
-  setenv ("EASYBUILD_UMASK", "022")
+  setenv ("EASYBUILD_UMASK", "077")
   setenv ("EASYBUILD_STICKY_BIT", "1")
   -- configure MODULEPATH
   if (project_modulepath ~= nil) then
@@ -155,6 +160,7 @@ elseif (project_modulepath ~= nil) then
   setenv ("EASYBUILD_SET_GID_BIT", "1")
   setenv ("EASYBUILD_GROUP_WRITABLE_INSTALLDIR", "1")
   setenv ("EASYBUILD_STICKY_BIT", "0")
+  setenv ("EASYBUILD_UMASK", "002")
   -- configure MODULEPATH
   prepend_path("MODULEPATH", project_modulepath)
 end
diff --git a/easystacks/software.eessi.io/2023.06/rebuilds/20240506-eb-4.9.1-EESSI-extend-allow-loaded.yml b/easystacks/software.eessi.io/2023.06/rebuilds/20240506-eb-4.9.1-EESSI-extend-allow-loaded.yml
new file mode 100644
index 0000000000..93c4950fc8
--- /dev/null
+++ b/easystacks/software.eessi.io/2023.06/rebuilds/20240506-eb-4.9.1-EESSI-extend-allow-loaded.yml
@@ -0,0 +1,5 @@
+# 2024.05.15
+# The module is an EasyBuild created module and therefore needs to be an allowed
+# module when running EasyBuild
+easyconfigs:
+  - EESSI-extend-2023.06-easybuild.eb