diff --git a/postgrest/_async/client.py b/postgrest/_async/client.py
index b9d266d..94c9c7f 100644
--- a/postgrest/_async/client.py
+++ b/postgrest/_async/client.py
@@ -60,6 +60,17 @@ def create_session(
             http2=True,
         )
 
+    def schema(self, schema: str):
+        """Switch to another schema."""
+        return AsyncPostgrestClient(
+            base_url=self.base_url,
+            schema=schema,
+            headers=self.headers,
+            timeout=self.timeout,
+            verify=self.verify,
+            proxy=self.proxy,
+        )
+
     async def __aenter__(self) -> AsyncPostgrestClient:
         return self
 
diff --git a/postgrest/_sync/client.py b/postgrest/_sync/client.py
index 29b9aab..a9dd307 100644
--- a/postgrest/_sync/client.py
+++ b/postgrest/_sync/client.py
@@ -60,6 +60,17 @@ def create_session(
             http2=True,
         )
 
+    def schema(self, schema: str):
+        """Switch to another schema."""
+        return SyncPostgrestClient(
+            base_url=self.base_url,
+            schema=schema,
+            headers=self.headers,
+            timeout=self.timeout,
+            verify=self.verify,
+            proxy=self.proxy,
+        )
+
     def __enter__(self) -> SyncPostgrestClient:
         return self
 
diff --git a/postgrest/_sync/request_builder.py b/postgrest/_sync/request_builder.py
index 8b0eb16..9683b1a 100644
--- a/postgrest/_sync/request_builder.py
+++ b/postgrest/_sync/request_builder.py
@@ -34,7 +34,7 @@ def __init__(
         http_method: str,
         headers: Headers,
         params: QueryParams,
-        json: Union[dict, list],
+        json: dict,
     ) -> None:
         self.session = session
         self.path = path
diff --git a/postgrest/base_client.py b/postgrest/base_client.py
index e2bf417..2c9756a 100644
--- a/postgrest/base_client.py
+++ b/postgrest/base_client.py
@@ -23,12 +23,19 @@ def __init__(
     ) -> None:
         if not is_http_url(base_url):
             ValueError("base_url must be a valid HTTP URL string")
-        headers = {
+
+        self.base_url = base_url
+        self.headers = {
             **headers,
             "Accept-Profile": schema,
             "Content-Profile": schema,
         }
-        self.session = self.create_session(base_url, headers, timeout, verify, proxy)
+        self.timeout = timeout
+        self.verify = verify
+        self.proxy = proxy
+        self.session = self.create_session(
+            self.base_url, self.headers, self.timeout, self.verify, self.proxy
+        )
 
     @abstractmethod
     def create_session(
@@ -68,13 +75,3 @@ def auth(
                 "Neither bearer token or basic authentication scheme is provided"
             )
         return self
-
-    def schema(self, schema: str):
-        """Switch to another schema."""
-        self.session.headers.update(
-            {
-                "Accept-Profile": schema,
-                "Content-Profile": schema,
-            }
-        )
-        return self
diff --git a/tests/_async/test_client.py b/tests/_async/test_client.py
index e99f348..fb7881c 100644
--- a/tests/_async/test_client.py
+++ b/tests/_async/test_client.py
@@ -62,8 +62,8 @@ def test_auth_basic(self, postgrest_client: AsyncPostgrestClient):
 
 
 def test_schema(postgrest_client: AsyncPostgrestClient):
-    postgrest_client.schema("private")
-    session = postgrest_client.session
+    client = postgrest_client.schema("private")
+    session = client.session
     subheaders = {
         "accept-profile": "private",
         "content-profile": "private",
diff --git a/tests/_sync/test_client.py b/tests/_sync/test_client.py
index 5c471c2..930fb7b 100644
--- a/tests/_sync/test_client.py
+++ b/tests/_sync/test_client.py
@@ -61,8 +61,8 @@ def test_auth_basic(self, postgrest_client: SyncPostgrestClient):
 
 
 def test_schema(postgrest_client: SyncPostgrestClient):
-    postgrest_client.schema("private")
-    session = postgrest_client.session
+    client = postgrest_client.schema("private")
+    session = client.session
     subheaders = {
         "accept-profile": "private",
         "content-profile": "private",