diff --git a/.github/workflows/testsuite_allprocesses.yml b/.github/workflows/testsuite_allprocesses.yml
index 7eaad09c9f..dbf0fdc4b3 100644
--- a/.github/workflows/testsuite_allprocesses.yml
+++ b/.github/workflows/testsuite_allprocesses.yml
@@ -37,5 +37,7 @@ jobs:
     uses: ./.github/workflows/testsuite_oneprocess.yml
     with:
       process: ${{ matrix.process }}.${{ matrix.suffix }}
+      # By default, in allprocesses tests enable FPE tests when pushing, but not in pull requests
+      enableFPE: ${{ github.event_name != 'pull_request' }}
 
 #----------------------------------------------------------------------------------------------------------------------------------
diff --git a/.github/workflows/testsuite_oneprocess.sh b/.github/workflows/testsuite_oneprocess.sh
index 639991f1cb..faff0538fe 100755
--- a/.github/workflows/testsuite_oneprocess.sh
+++ b/.github/workflows/testsuite_oneprocess.sh
@@ -203,8 +203,8 @@ function tput_test() {
     echo "Testing in $(pwd)"
     # FIXME1: this is just a quick test, eventually port here tput tests from throughputX.sh
     # (could move some throughputX.sh functions to a separate script included both here and there)
-    # FIXME2: enable FPEs
-    # FIXME3: handle all d/f/m, inl0/1, hrd0/1 etc...
+    # FIXME2: handle all d/f/m, inl0/1, hrd0/1 etc...
+    # FIXME3: add fcheck.exe tests
     unamep=$(uname -p)
     unames=$(uname -s)
     for simd in none sse4 avx2 512y 512z; do
@@ -233,6 +233,11 @@ function tput_test() {
   done
 }
 
+# Tput-test with FPEs enabled
+function tput_test_fpe() {
+  CUDACPP_RUNTIME_ENABLEFPE=1 tput_test $*
+}
+
 #----------------------------------------------------------------------------------------------------------------------------------
 
 # Usage
@@ -244,7 +249,7 @@ function usage() {
 #----------------------------------------------------------------------------------------------------------------------------------
 
 # Valid stages
-stages="codegen before_build build after_build tput_test"
+stages="codegen before_build build after_build tput_test tput_test_fpe"
 
 # Check input arguments
 for astage in $stages; do
diff --git a/.github/workflows/testsuite_oneprocess.yml b/.github/workflows/testsuite_oneprocess.yml
index 0d0973f210..17dc783b63 100644
--- a/.github/workflows/testsuite_oneprocess.yml
+++ b/.github/workflows/testsuite_oneprocess.yml
@@ -10,7 +10,7 @@ name: Test one process
 #----------------------------------------------------------------------------------------------------------------------------------
 
 # See https://docs.github.com/en/actions/using-workflows/workflow-syntax-for-github-actions#run-name
-run-name: Manually test one process ${{ inputs.process }}
+run-name: Manually test one process ${{ inputs.process }} (enableFPE = ${{ inputs.enableFPE }}) 
 
 #----------------------------------------------------------------------------------------------------------------------------------
 
@@ -23,19 +23,26 @@ on:
       process: # this variable is provided by the matrix in testsuite_allprocesses.yml
         required: true
         type: string
+      enableFPE:
+        required: true
+        type: boolean
 
   # Manually trigger the one-process workflow
   # (the lines below are adapted rom the default github manual workflow example)
   workflow_dispatch:
     inputs:
       process:
-        description: 'Physics process'
+        description: 'physics process'
         default: 'gg_tt.mad'
         required: true
-        ###type: string
         type: choice
         # FIXME? Can the list of supported processes be specified only once in oneprocess.yml or allprocesses.yml?
-        options: [gg_tt.mad, gg_ttg.mad, gg_ttgg.mad, gg_ttggg.mad, ee_mumu.mad]
+        options: [ee_mumu.mad, gg_tt.mad, gg_ttg.mad, gg_ttgg.mad, gg_ttggg.mad, gg_tt01g.mad, gq_ttq.mad, pp_tt012j.mad]
+      enableFPE:
+        description: 'enable FPE tests?'
+        default: true
+        required: true
+        type: boolean
 
 #----------------------------------------------------------------------------------------------------------------------------------
 
@@ -134,6 +141,10 @@ jobs:
     - name: tput_test
       run: .github/workflows/testsuite_oneprocess.sh tput_test ${{ inputs.process }}
 
+    - name: tput_test_fpe
+      run: .github/workflows/testsuite_oneprocess.sh tput_test_fpe ${{ inputs.process }}
+      if: ${{ inputs.enableFPE }}
+
     - name: GOODBYE
       run: |
         echo "GOODBYE ${{ inputs.process }}! $(date)"