diff --git a/django/contrib/postgres/search.py b/django/contrib/postgres/search.py
index 4628f4cf19..fb2f41b524 100644
--- a/django/contrib/postgres/search.py
+++ b/django/contrib/postgres/search.py
@@ -92,14 +92,43 @@ class CombinedSearchVector(SearchVectorCombinable, CombinedExpression):
         super(CombinedSearchVector, self).__init__(lhs, connector, rhs, output_field)
 
 
-class SearchQuery(Value):
+class SearchQueryCombinable(object):
+    BITAND = '&&'
+    BITOR = '||'
+
+    def _combine(self, other, connector, reversed, node=None):
+        if not isinstance(other, SearchQueryCombinable):
+            raise TypeError(
+                'SearchQuery can only be combined with other SearchQuerys, '
+                'got {}.'.format(type(other))
+            )
+        if not self.config == other.config:
+            raise TypeError("SearchQuery configs don't match.")
+        if reversed:
+            return CombinedSearchQuery(other, connector, self, self.config)
+        return CombinedSearchQuery(self, connector, other, self.config)
+
+    # On Combinable, these are not implemented to reduce confusion with Q. In
+    # this case we are actually (ab)using them to do logical combination so
+    # it's consistent with other usage in Django.
+    def __or__(self, other):
+        return self._combine(other, self.BITOR, False)
+
+    def __ror__(self, other):
+        return self._combine(other, self.BITOR, True)
+
+    def __and__(self, other):
+        return self._combine(other, self.BITAND, False)
+
+    def __rand__(self, other):
+        return self._combine(other, self.BITAND, True)
+
+
+class SearchQuery(SearchQueryCombinable, Value):
     invert = False
     _output_field = SearchQueryField()
     config = None
 
-    BITAND = '&&'
-    BITOR = '||'
-
     def __init__(self, value, output_field=None, **extra):
         self.config = extra.pop('config', self.config)
         self.invert = extra.pop('invert', self.invert)
@@ -131,21 +160,6 @@ class SearchQuery(Value):
         combined.output_field = SearchQueryField()
         return combined
 
-    # On Combinable, these are not implemented to reduce confusion with Q. In
-    # this case we are actually (ab)using them to do logical combination so
-    # it's consistent with other usage in Django.
-    def __or__(self, other):
-        return self._combine(other, self.BITOR, False)
-
-    def __ror__(self, other):
-        return self._combine(other, self.BITOR, True)
-
-    def __and__(self, other):
-        return self._combine(other, self.BITAND, False)
-
-    def __rand__(self, other):
-        return self._combine(other, self.BITAND, True)
-
     def __invert__(self):
         extra = {
             'invert': not self.invert,
@@ -154,6 +168,12 @@ class SearchQuery(Value):
         return type(self)(self.value, **extra)
 
 
+class CombinedSearchQuery(SearchQueryCombinable, CombinedExpression):
+    def __init__(self, lhs, connector, rhs, config, output_field=None):
+        self.config = config
+        super(CombinedSearchQuery, self).__init__(lhs, connector, rhs, output_field)
+
+
 class SearchRank(Func):
     function = 'ts_rank'
     _output_field = FloatField()
diff --git a/docs/releases/1.10.2.txt b/docs/releases/1.10.2.txt
index f3c574d7d1..bc11980053 100644
--- a/docs/releases/1.10.2.txt
+++ b/docs/releases/1.10.2.txt
@@ -11,3 +11,6 @@ Bugfixes
 
 * Fixed a crash in MySQL database validation where ``SELECT @@sql_mode``
   doesn't return a result (:ticket:`27180`).
+
+* Allowed combining ``contrib.postgres.search.SearchQuery`` with more than one
+  ``&`` or ``|`` operators (:ticket:`27143`).
diff --git a/tests/postgres_tests/test_search.py b/tests/postgres_tests/test_search.py
index 93d86bf275..0bf2df50f1 100644
--- a/tests/postgres_tests/test_search.py
+++ b/tests/postgres_tests/test_search.py
@@ -205,14 +205,46 @@ class TestCombinations(GrailTestData, PostgreSQLTestCase):
         ).filter(search=SearchQuery('bedemir') & SearchQuery('scales'))
         self.assertSequenceEqual(searched, [self.bedemir0])
 
+    def test_query_multiple_and(self):
+        searched = Line.objects.annotate(
+            search=SearchVector('scene__setting', 'dialogue'),
+        ).filter(search=SearchQuery('bedemir') & SearchQuery('scales') & SearchQuery('nostrils'))
+        self.assertSequenceEqual(searched, [])
+
+        searched = Line.objects.annotate(
+            search=SearchVector('scene__setting', 'dialogue'),
+        ).filter(search=SearchQuery('shall') & SearchQuery('use') & SearchQuery('larger'))
+        self.assertSequenceEqual(searched, [self.bedemir0])
+
     def test_query_or(self):
         searched = Line.objects.filter(dialogue__search=SearchQuery('kneecaps') | SearchQuery('nostrils'))
         self.assertSequenceEqual(set(searched), {self.verse1, self.verse2})
 
+    def test_query_multiple_or(self):
+        searched = Line.objects.filter(
+            dialogue__search=SearchQuery('kneecaps') | SearchQuery('nostrils') | SearchQuery('Sir Robin')
+        )
+        self.assertSequenceEqual(set(searched), {self.verse1, self.verse2, self.verse0})
+
     def test_query_invert(self):
         searched = Line.objects.filter(character=self.minstrel, dialogue__search=~SearchQuery('kneecaps'))
         self.assertEqual(set(searched), {self.verse0, self.verse2})
 
+    def test_query_config_mismatch(self):
+        with self.assertRaisesMessage(TypeError, "SearchQuery configs don't match."):
+            Line.objects.filter(
+                dialogue__search=SearchQuery('kneecaps', config='german') |
+                SearchQuery('nostrils', config='english')
+            )
+
+    def test_query_combined_mismatch(self):
+        msg = "SearchQuery can only be combined with other SearchQuerys, got"
+        with self.assertRaisesMessage(TypeError, msg):
+            Line.objects.filter(dialogue__search=None | SearchQuery('kneecaps'))
+
+        with self.assertRaisesMessage(TypeError, msg):
+            Line.objects.filter(dialogue__search=None & SearchQuery('kneecaps'))
+
 
 @modify_settings(INSTALLED_APPS={'append': 'django.contrib.postgres'})
 class TestRankingAndWeights(GrailTestData, PostgreSQLTestCase):