This is well outside my area of expertise, so please correct me if I'm wrong. But my understanding was that the legal parties are all subservient to the CCP and acknowledge their primacy.
So functionally maybe a little like Albertson's is the only legal party, but if you prefer your region can have a subsidiary of Albertson's like Safeway or Shaw's.
Officially no, effectively yes. It is not like they have meaningful elections, so a lot of power brokering is done behind doors. They do, however, provide minority parties with a quota of seats, although they effectively don't have decision making power (like the governor of a province vs. the CPC chairman of the province).
So functionally maybe a little like Albertson's is the only legal party, but if you prefer your region can have a subsidiary of Albertson's like Safeway or Shaw's.