diff --git a/src/ert/gui/tools/manage_experiments/manage_experiments_panel.py b/src/ert/gui/tools/manage_experiments/manage_experiments_panel.py
index 8f833db2248..1564a1238c1 100644
--- a/src/ert/gui/tools/manage_experiments/manage_experiments_panel.py
+++ b/src/ert/gui/tools/manage_experiments/manage_experiments_panel.py
@@ -67,7 +67,7 @@ def headerData(
             orientation == Qt.Orientation.Horizontal
             and role == Qt.ItemDataRole.DisplayRole
         ):
-            return self._df.columns[section]
+            return "\n".join(self._df.columns[section])
         return QtCore.QVariant()
 
 
diff --git a/src/ert/sensitivity_analysis/design_matrix.py b/src/ert/sensitivity_analysis/design_matrix.py
index cf40b51e5d3..1fc928d29b5 100644
--- a/src/ert/sensitivity_analysis/design_matrix.py
+++ b/src/ert/sensitivity_analysis/design_matrix.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+from collections import defaultdict
 from pathlib import Path
 from typing import TYPE_CHECKING
 
@@ -49,18 +50,40 @@ def read_design_matrix(
     # ignoring errors here is deprecated in pandas, should find another solution
     # design_matrix_sheet = design_matrix_sheet.apply(pd.to_numeric, errors="ignore")
 
-    existing_parameters = {
-        param.name
+    parameter_groups = defaultdict(list)
+    parameter_map = []
+    all_param_configs = [
+        param_group
         for param_group in ert_config.ensemble_config.parameter_configuration
         if isinstance(param_group, GenKwConfig)
-        for param in param_group.transform_function_definitions
-    }
-    intersect = existing_parameters.intersection(set(design_matrix_sheet.columns))
-    # This errors if parameters exists already, this behaviour should be discussed.
-    if intersect:
-        msg = "The following parameters were specified both"
-        f"as gen_kw and in the design matrix: {intersect}"
+    ]
+    errors = {}
+    for param in design_matrix_sheet.columns:
+        par_gp = []
+        for param_group in all_param_configs:
+            if param in param_group:
+                par_gp.append(param_group.name)
+
+        if not par_gp:
+            parameter_name = "DESIGN_MATRIX"
+            parameter_groups[parameter_name].append(param)
+            parameter_map.append((parameter_name, param))
+        elif len(par_gp) == 1:
+            parameter_name = par_gp[0]
+            parameter_groups[parameter_name].append(param)
+            parameter_map.append((parameter_name, param))
+        else:
+            errors[param] = par_gp
+
+    if errors:
+        msg = ""
+        for key, value in errors.items():
+            msg += (
+                f"The following parameter '{key}' was found in multiple"
+                f" GenKw parameters groups: {value}."
+            )
         raise ValueError(msg)
+    design_matrix_sheet.columns = pd.MultiIndex.from_tuples(parameter_map)
     return design_matrix_sheet
 
 
@@ -71,30 +94,34 @@ def initialize_parameters(
     exp_name: str,
     ens_name: str,
 ) -> LocalEnsemble:
-    existing_parameters = ert_config.ensemble_config.parameter_configuration
-    parameters = design_matrix_sheet.columns
-    transform_function_definitions: list[TransformFunctionDefinition] = []
-    for param in parameters:
-        transform_function_definitions.append(
-            TransformFunctionDefinition(
-                name=param,
-                param_name="RAW",
-                values=[],
+    existing_parameters = ert_config.ensemble_config.parameter_configs.copy()
+    for parameter_group in design_matrix_sheet.columns.get_level_values(0).unique():
+        parameters = design_matrix_sheet[parameter_group].columns
+        transform_function_definitions: list[TransformFunctionDefinition] = []
+        for param in parameters:
+            transform_function_definitions.append(
+                TransformFunctionDefinition(
+                    name=param,
+                    param_name="RAW",
+                    values=[],
+                )
             )
-        )
-    existing_parameters.append(
-        GenKwConfig(
-            name=DESIGN_MATRIX_GROUP,
+        existing = existing_parameters.get(parameter_group)
+        existing_parameters[parameter_group] = GenKwConfig(
+            name=parameter_group,
             forward_init=False,
-            template_file=None,
-            output_file=None,
+            template_file=existing.template_file
+            if isinstance(existing, GenKwConfig)
+            else None,
+            output_file=existing.output_file
+            if isinstance(existing, GenKwConfig)
+            else None,
             transform_function_definitions=transform_function_definitions,
             update=False,
         )
-    )
 
     experiment = storage.create_experiment(
-        parameters=existing_parameters,
+        parameters=list(existing_parameters.values()),
         responses=ert_config.ensemble_config.response_configuration,
         observations=ert_config.observations,
         name=exp_name,
@@ -105,15 +132,16 @@ def initialize_parameters(
         ensemble_size=len(design_matrix_sheet.index),
     )
     for i in design_matrix_sheet.index:
-        row: pd.Series = design_matrix_sheet.iloc[i]
-        ds = xr.Dataset(
-            {
-                "values": ("names", list(row.to_numpy())),
-                "transformed_values": ("names", list(row.to_numpy())),
-                "names": list(row.keys()),
-            }
-        )
-        ensemble.save_parameters(DESIGN_MATRIX_GROUP, i, ds)
+        for parameter_group in experiment.parameter_configuration:
+            row: pd.Series = design_matrix_sheet.iloc[i][parameter_group]
+            ds = xr.Dataset(
+                {
+                    "values": ("names", list(row.to_numpy())),
+                    "transformed_values": ("names", list(row.to_numpy())),
+                    "names": list(row.keys()),
+                }
+            )
+            ensemble.save_parameters(parameter_group, i, ds)
     return ensemble
 
 
diff --git a/tests/unit_tests/sensitivity_analysis/test_design_matrix.py b/tests/ert/unit_tests/sensitivity_analysis/test_design_matrix.py
similarity index 97%
rename from tests/unit_tests/sensitivity_analysis/test_design_matrix.py
rename to tests/ert/unit_tests/sensitivity_analysis/test_design_matrix.py
index 502f4d76099..95429da1b60 100644
--- a/tests/unit_tests/sensitivity_analysis/test_design_matrix.py
+++ b/tests/ert/unit_tests/sensitivity_analysis/test_design_matrix.py
@@ -23,6 +23,7 @@ def test_design_matrix(copy_poly_case):
 NUM_REALIZATIONS 100
 MIN_REALIZATIONS 1
 
+GEN_KW COEFFS coeff_priors
 GEN_DATA POLY_RES RESULT_FILE:poly.out
 
 INSTALL_JOB poly_eval POLY_EVAL