diff --git a/cosmos/converter.py b/cosmos/converter.py
index dbc290271..45d98a4cf 100644
--- a/cosmos/converter.py
+++ b/cosmos/converter.py
@@ -3,6 +3,7 @@
 
 from __future__ import annotations
 
+import copy
 import inspect
 from typing import Any, Callable
 
@@ -118,6 +119,10 @@ def __init__(
         # If we are using the old interface, we should migrate it to the new interface
         # This is safe to do now since we have validated which config interface we're using
         if project_config.dbt_project_path:
+            # We copy the configuration so the change does not affect other DAGs or TaskGroups
+            # that may reuse the same original configuration
+            render_config = copy.deepcopy(render_config)
+            execution_config = copy.deepcopy(execution_config)
             render_config.project_path = project_config.dbt_project_path
             execution_config.project_path = project_config.dbt_project_path
 
diff --git a/dev/dags/basic_cosmos_task_group.py b/dev/dags/basic_cosmos_task_group.py
index 50cb6ed09..731914953 100644
--- a/dev/dags/basic_cosmos_task_group.py
+++ b/dev/dags/basic_cosmos_task_group.py
@@ -2,13 +2,14 @@
 An example DAG that uses Cosmos to render a dbt project as a TaskGroup.
 """
 import os
+
 from datetime import datetime
 from pathlib import Path
 
 from airflow.decorators import dag
 from airflow.operators.empty import EmptyOperator
 
-from cosmos import DbtTaskGroup, ProjectConfig, ProfileConfig
+from cosmos import DbtTaskGroup, ProjectConfig, ProfileConfig, RenderConfig, ExecutionConfig
 from cosmos.profiles import PostgresUserPasswordProfileMapping
 
 DEFAULT_DBT_ROOT_PATH = Path(__file__).parent / "dbt"
@@ -23,6 +24,8 @@
     ),
 )
 
+shared_execution_config = ExecutionConfig()
+
 
 @dag(
     schedule_interval="@daily",
@@ -35,11 +38,25 @@ def basic_cosmos_task_group() -> None:
     """
     pre_dbt = EmptyOperator(task_id="pre_dbt")
 
-    jaffle_shop = DbtTaskGroup(
-        group_id="test_123",
+    customers = DbtTaskGroup(
+        group_id="customers",
+        project_config=ProjectConfig(
+            (DBT_ROOT_PATH / "jaffle_shop").as_posix(),
+        ),
+        render_config=RenderConfig(select=["path:seeds/raw_customers.csv"]),
+        execution_config=shared_execution_config,
+        operator_args={"install_deps": True},
+        profile_config=profile_config,
+        default_args={"retries": 2},
+    )
+
+    orders = DbtTaskGroup(
+        group_id="orders",
         project_config=ProjectConfig(
             (DBT_ROOT_PATH / "jaffle_shop").as_posix(),
         ),
+        render_config=RenderConfig(select=["path:seeds/raw_orders.csv"]),
+        execution_config=shared_execution_config,
         operator_args={"install_deps": True},
         profile_config=profile_config,
         default_args={"retries": 2},
@@ -47,7 +64,8 @@ def basic_cosmos_task_group() -> None:
 
     post_dbt = EmptyOperator(task_id="post_dbt")
 
-    pre_dbt >> jaffle_shop >> post_dbt
+    pre_dbt >> customers >> post_dbt
+    pre_dbt >> orders >> post_dbt
 
 
 basic_cosmos_task_group()