diff --git a/easybuild/tools/toolchain/mpi.py b/easybuild/tools/toolchain/mpi.py
index 2f501d2fec..35ecc28188 100644
--- a/easybuild/tools/toolchain/mpi.py
+++ b/easybuild/tools/toolchain/mpi.py
@@ -48,7 +48,7 @@
 _log = fancylogger.getLogger('tools.toolchain.mpi', fname=False)
 
 
-def get_mpi_cmd_template(mpi_family, params, mpi_version=None):
+def get_mpi_cmd_template(mpi_family, params, mpi_version=None, oversubscribe=False):
     """
     Return template for MPI command, for specified MPI family.
 
@@ -123,6 +123,50 @@ def get_mpi_cmd_template(mpi_family, params, mpi_version=None):
         else:
             raise EasyBuildError("Don't know which template MPI command to use for MPI family '%s'", mpi_family)
 
+        if oversubscribe:
+            osub_cmd = ''
+            if mpi_family in [toolchain.OPENMPI]:
+                if mpi_version is None:
+                    raise EasyBuildError("OpenMPI version unknown, can't determine how to handle oversubscription!")
+                if LooseVersion(mpi_version) < '5':
+                    varname = 'OMPI_MCA_rmaps_base_oversubscribe'
+                    varvalue = os.getenv(varname)
+                    if varvalue and varvalue != '1':
+                        _log.warning("Overwriting existing %s=%s with %s=1", varname, varvalue, varname)
+                    osub_cmd = f'{varname}=1'
+                else:
+                    varname = 'PRTE_MCA_rmaps_default_mapping_policy'
+                    varvalue = os.getenv(varname)
+
+                    # This logic should account for:
+                    # - var not set -> set to 'core:oversubscribe'
+                    # - unit set to value without `:` eg package -> 'package:oversubscribe'
+                    # - unit set to value with `:` eg ppr:4:numa -> 'ppr:4:numa:oversubscribe'
+                    # - all of the above but with oversubscribe already in flags
+                    flags = ''
+                    if varvalue.startswith('ppr'):
+                        _log.warning("Can't handle ppr mapping with oversubscription yet, overwriting unit with 'core'")
+                        unit = 'core'
+                        flags = 'oversubscribe'
+                    else:
+                        unit, flags = (varvalue.rsplit(':', maxsplit=1) + [''])[:2]
+                    unit = unit or 'core'
+                    flags = list(filter(None, flags.split(',')))
+                    if 'oversubscribe' not in flags:
+                        flags.append('oversubscribe')
+                    newvalue = f"{unit}:{','.join(flags)}"
+
+                    osub_cmd = f'{varname}={newvalue}'
+            elif mpi_family in [toolchain.INTELMPI]:
+                _log.info("INTELMPI always oversubscribe by default, nothing to do...")
+            elif mpi_family in [toolchain.MVAPICH2, toolchain.MPICH, toolchain.MPICH2]:
+                _log.info("MPICH always oversubscribe by default, nothing to do...")
+            else:
+                raise EasyBuildError("Oversubscribe not supported for MPI family '%s'", mpi_family)
+
+            mpi_cmd_template = f'%(oversubscribe)s {mpi_cmd_template}'
+            params.update({'oversubscribe': osub_cmd})  # just a placeholder
+
     missing = []
     for key in sorted(params.keys()):
         tmpl = '%(' + key + ')s'
@@ -270,7 +314,7 @@ def mpi_cmd_prefix(self, nr_ranks=1):
 
         return result
 
-    def mpi_cmd_for(self, cmd, nr_ranks):
+    def mpi_cmd_for(self, cmd, nr_ranks, oversubscribe=False):
         """Construct an MPI command for the given command and number of ranks."""
 
         # parameter values for mpirun command
@@ -281,20 +325,20 @@ def mpi_cmd_for(self, cmd, nr_ranks):
 
         mpi_family = self.mpi_family()
 
-        mpi_version = None
+        # this fails when it's done too early (before modules for toolchain/dependencies are loaded),
+        # but it's safe to ignore this
+        mpi_version = self.get_software_version(self.MPI_MODULE_NAME, required=False)[0]
 
         if mpi_family == toolchain.INTELMPI:
-            # for Intel MPI, try to determine impi version
-            # this fails when it's done too early (before modules for toolchain/dependencies are loaded),
-            # but it's safe to ignore this
-            mpi_version = self.get_software_version(self.MPI_MODULE_NAME, required=False)[0]
             if not mpi_version:
                 self.log.debug("Ignoring error when trying to determine %s version", self.MPI_MODULE_NAME)
                 # impi version is required to determine correct MPI command template,
                 # so we have to return early if we couldn't determine the impi version...
                 return None
 
-        mpi_cmd_template, params = get_mpi_cmd_template(mpi_family, params, mpi_version=mpi_version)
+        mpi_cmd_template, params = get_mpi_cmd_template(
+            mpi_family, params, mpi_version=mpi_version, oversubscribe=oversubscribe
+        )
         self.log.info("Using MPI command template '%s' (params: %s)", mpi_cmd_template, params)
 
         try: