I am a licensed real estate broker in CA working as a Broker-Salesperson for a company.

From my understanding of the rights of a licensed broker, the DRE states that a Broker can work for him/herself as well as multiple companies at the same time.

1.) Can anybody chime in on this who's a real estate broker in CA?

2.) Is it possible to work under a Coldwell Banker and lets say Keller Williams at the same time?

3.) My question is if I can work for myself as a Broker, while also being under another company, what are the rules in choosing who to work under for each transaction.

4.) Furthermore, since I can also work under myself, lets say that I have a client who is going to purchase a property. If I put the offer through under my own name instead of the real estate company that I am also licensed under, then I don't have to pay the commission split for that transaction. Is this permitted?