diff --git a/django/contrib/gis/db/models/lookups.py b/django/contrib/gis/db/models/lookups.py
index 3f3bc8acc8aa8..2f382acf913ec 100644
--- a/django/contrib/gis/db/models/lookups.py
+++ b/django/contrib/gis/db/models/lookups.py
@@ -1,7 +1,7 @@
 import re
 
 from django.contrib.gis.db.models.fields import BaseSpatialField
-from django.db.models.expressions import Col, Expression
+from django.db.models.expressions import Expression
 from django.db.models.lookups import Lookup, Transform
 from django.db.models.sql.query import Query
 
@@ -55,30 +55,19 @@ def process_band_indices(self, only_lhs=False):
 
     def get_db_prep_lookup(self, value, connection):
         # get_db_prep_lookup is called by process_rhs from super class
-        return ('%s', [connection.ops.Adapter(value)] + (self.rhs_params or []))
+        return ('%s', [connection.ops.Adapter(value)])
 
     def process_rhs(self, compiler, connection):
         if isinstance(self.rhs, Query):
             # If rhs is some Query, don't touch it.
             return super().process_rhs(compiler, connection)
 
-        geom = self.rhs
-        if isinstance(self.rhs, Col):
-            # Make sure the F Expression destination field exists, and
-            # set an `srid` attribute with the same as that of the
-            # destination.
-            geo_fld = self.rhs.output_field
-            if not hasattr(geo_fld, 'srid'):
-                raise ValueError('No geographic field found in expression.')
-            self.rhs.srid = geo_fld.srid
-            sql, _ = compiler.compile(geom)
-            return connection.ops.get_geom_placeholder(self.lhs.output_field, geom, compiler) % sql, []
-        elif isinstance(self.rhs, Expression):
-            raise ValueError('Complex expressions not supported for spatial fields.')
+        if isinstance(self.rhs, Expression):
+            self.rhs = self.rhs.resolve_expression(compiler.query)
 
         rhs, rhs_params = super().process_rhs(compiler, connection)
-        rhs = connection.ops.get_geom_placeholder(self.lhs.output_field, geom, compiler)
-        return rhs, rhs_params
+        placeholder = connection.ops.get_geom_placeholder(self.lhs.output_field, self.rhs, compiler)
+        return placeholder % rhs, rhs_params
 
     def get_rhs_op(self, connection, rhs):
         # Unlike BuiltinLookup, the GIS get_rhs_op() implementation should return
@@ -267,18 +256,17 @@ class RelateLookup(GISLookup):
     sql_template = '%(func)s(%(lhs)s, %(rhs)s, %%s)'
     pattern_regex = re.compile(r'^[012TF\*]{9}$')
 
-    def get_db_prep_lookup(self, value, connection):
-        if len(self.rhs_params) != 1:
-            raise ValueError('relate must be passed a two-tuple')
+    def process_rhs(self, compiler, connection):
         # Check the pattern argument
+        pattern = self.rhs_params[0]
         backend_op = connection.ops.gis_operators[self.lookup_name]
         if hasattr(backend_op, 'check_relate_argument'):
-            backend_op.check_relate_argument(self.rhs_params[0])
-        else:
-            pattern = self.rhs_params[0]
-            if not isinstance(pattern, str) or not self.pattern_regex.match(pattern):
-                raise ValueError('Invalid intersection matrix pattern "%s".' % pattern)
-        return super().get_db_prep_lookup(value, connection)
+            backend_op.check_relate_argument(pattern)
+        elif not isinstance(pattern, str) or not self.pattern_regex.match(pattern):
+            raise ValueError('Invalid intersection matrix pattern "%s".' % pattern)
+
+        sql, params = super().process_rhs(compiler, connection)
+        return sql, params + [pattern]
 
 
 @BaseSpatialField.register_lookup
@@ -322,8 +310,8 @@ class DWithinLookup(DistanceLookupBase):
     def process_rhs(self, compiler, connection):
         dist_sql, dist_params = self.process_distance(compiler, connection)
         self.template_params['value'] = dist_sql
-        rhs = connection.ops.get_geom_placeholder(self.lhs.output_field, self.rhs, compiler)
-        return rhs, [connection.ops.Adapter(self.rhs)] + dist_params
+        rhs_sql, params = super().process_rhs(compiler, connection)
+        return rhs_sql, params + dist_params
 
 
 class DistanceLookupFromFunction(DistanceLookupBase):
diff --git a/tests/gis_tests/distapp/tests.py b/tests/gis_tests/distapp/tests.py
index ec6c40eac3890..395f7226ef429 100644
--- a/tests/gis_tests/distapp/tests.py
+++ b/tests/gis_tests/distapp/tests.py
@@ -73,6 +73,9 @@ def test_dwithin(self):
                 with self.subTest(dist=dist, qs=qs):
                     self.assertEqual(tx_cities, self.get_names(qs))
 
+        # With a complex geometry expression
+        self.assertFalse(SouthTexasCity.objects.exclude(point__dwithin=(Union('point', 'point'), 0)))
+
         # Now performing the `dwithin` queries on a geodetic coordinate system.
         for dist in au_dists:
             with self.subTest(dist=dist):
diff --git a/tests/gis_tests/geoapp/tests.py b/tests/gis_tests/geoapp/tests.py
index 1e6d111ba5d74..6bff300837b3a 100644
--- a/tests/gis_tests/geoapp/tests.py
+++ b/tests/gis_tests/geoapp/tests.py
@@ -448,6 +448,18 @@ def test_relate_lookup(self):
             self.assertEqual('Texas', Country.objects.get(mpoly__relate=(pnt2, intersects_mask)).name)
             self.assertEqual('Lawrence', City.objects.get(point__relate=(ks.poly, intersects_mask)).name)
 
+        # With a complex geometry expression
+        mask = 'anyinteract' if oracle else within_mask
+        self.assertFalse(City.objects.exclude(point__relate=(functions.Union('point', 'point'), mask)))
+
+    def test_gis_lookups_with_complex_expressions(self):
+        multiple_arg_lookups = {'dwithin', 'relate'}  # These lookups are tested in other places.
+        lookups = connection.ops.gis_operators.keys() - multiple_arg_lookups
+        self.assertTrue(lookups, 'No lookups found')
+        for lookup in lookups:
+            with self.subTest(lookup):
+                City.objects.filter(**{'point__' + lookup: functions.Union('point', 'point')}).exists()
+
 
 class GeoQuerySetTest(TestCase):
     # TODO: GeoQuerySet is removed, organize these test better.