diff --git a/.github/workflows/tests_scripts.yml b/.github/workflows/tests_scripts.yml
index b1d2426774..4944d9beaa 100644
--- a/.github/workflows/tests_scripts.yml
+++ b/.github/workflows/tests_scripts.yml
@@ -5,6 +5,7 @@ on:
     paths:
       - build_container.sh
       - create_directory_tarballs.sh
+      - create_lmodsitepackage.py
       - EESSI-install-software.sh
       - install_software_layer.sh
       - load_easybuild_module.sh
@@ -16,6 +17,7 @@ on:
     paths:
       - build_container.sh
       - create_directory_tarballs.sh
+      - create_lmodsitepackage.py
       - EESSI-install-software.sh
       - install_software_layer.sh
       - load_easybuild_module.sh
@@ -96,3 +98,24 @@ jobs:
           ./eessi_container.sh --mode run --verbose /software-layer/create_directory_tarballs.sh 2023.06
           # check if tarballs have been produced
           ls -l *.tar.gz
+
+    - name: test create_lmodsitepackage.py script
+      run: |
+          # bind current directory into container as /software-layer
+          export SINGULARITY_BIND="${PWD}:/software-layer"
+
+          # Creates .lmod/SitePackage.lua in current dir, which then gets bind-mounted into /software-layer
+          python3 create_lmodsitepackage.py .
+          # run some commands to make sure that generated Lmod SitePackage file works
+          test_script="${PWD}/test_lmod_sitepackage.sh"
+          echo '#!/bin/bash' > ${test_script}
+          echo 'export LMOD_PACKAGE_PATH="/software-layer/.lmod"' > ${test_script}
+          echo 'ml --config' >> ${test_script}
+
+          chmod u+x ${test_script}
+
+          out="${PWD}/test_create_lmodsitepackage.out"
+          ./eessi_container.sh --mode run --verbose /software-layer/run_in_compat_layer_env.sh /software-layer/test_lmod_sitepackage.sh 2>&1 | tee ${out}
+          for pattern in "^Site Pkg location.*/software-layer/.lmod/SitePackage.lua" "LMOD_SITEPACKAGE_LOCATION.*/software-layer/.lmod/SitePackage.lua"; do
+            grep "${pattern}" ${out} || (echo "Pattern '${pattern}' not found in output!" && exit 1)
+          done
diff --git a/create_lmodsitepackage.py b/create_lmodsitepackage.py
index 5a7a915494..29b2d39bd7 100755
--- a/create_lmodsitepackage.py
+++ b/create_lmodsitepackage.py
@@ -19,6 +19,71 @@
     return content
 end
 
+local function load_site_specific_hooks()
+    -- This function will be run after the EESSI hooks are registered
+    -- It will load a local SitePackage.lua that is architecture independent (if it exists) from e.g.
+    -- /cvmfs/software.eessi.io/host_injections/2023.06/.lmod/SitePackage.lua
+    -- That can define a new hook
+    --
+    -- function site_specific_load_hook(t)
+    --     <some_action_on_load>
+    -- end
+    --
+    -- And the either append to the existing hook:
+    --
+    -- local function final_load_hook(t)
+    --    eessi_load_hook(t)
+    --    site_specific_load_hook(t)
+    -- end
+    --
+    -- Over overwrite the EESSI hook entirely:
+    --
+    -- hook.register("load", final_load_hook)
+    --
+    -- Note that the appending procedure can be simplified once we have an lmod >= 8.7.36
+    -- See https://github.com/TACC/Lmod/pull/696#issuecomment-1998765722
+    --
+    -- Subsequently, this function will look for an architecture-specific SitePackage.lua, e.g. from
+    -- /cvmfs/software.eessi.io/host_injections/2023.06/software/linux/x86_64/amd/zen2/.lmod/SitePackage.lua
+    -- This can then register an additional hook, e.g.
+    --
+    -- function arch_specific_load_hook(t)
+    --     <some_action_on_load>
+    -- end
+    --
+    -- local function final_load_hook(t)
+    --   eessi_load_hook(t)
+    --   site_specific_load_hook(t)
+    --   arch_specific_load_hook(t)
+    -- end
+    --
+    -- hook.register("load", final_load_hook)
+    --
+    -- Again, the host site could also decide to overwrite by simply doing
+    --
+    -- hook.register("load", arch_specific_load_hook)
+
+    -- get path to to architecture independent SitePackage.lua
+    local prefixHostInjections = string.gsub(os.getenv('EESSI_PREFIX') or "", 'versions', 'host_injections')
+    local hostSitePackage = prefixHostInjections .. "/.lmod/SitePackage.lua"
+
+    -- If the file exists, run it
+    if isFile(hostSitePackage) then
+        dofile(hostSitePackage)
+    end
+
+    -- build the full architecture specific path in host_injections
+    local archHostInjections = string.gsub(os.getenv('EESSI_SOFTWARE_PATH') or "", 'versions', 'host_injections')
+    local archSitePackage = archHostInjections .. "/.lmod/SitePackage.lua"
+
+    -- If the file exists, run it
+    if isFile(archSitePackage) then
+        dofile(archSitePackage)
+    end
+    
+end
+
+
 local function eessi_cuda_enabled_load_hook(t)
     local frameStk  = require("FrameStk"):singleton()
     local mt        = frameStk:mt()
@@ -92,6 +157,9 @@
 
 
 hook.register("load", eessi_load_hook)
+
+-- Note that this needs to happen at the end, so that any EESSI specific hooks can be overwritten by the site
+load_site_specific_hooks()
 """
 
 def error(msg):