Can California Intrastate Carrier book loads without MC Number/Authority?

I have a small fleet of two trucks that are leased onto a local carrier in the San Francisco Bay Area and was doing some research about getting my own authority to haul interstate. In that quest I came across Double Yellow's thread which also helped a lot(shoutout to him) , but my question is can a Intrastate Carrier haul loads for a broker as long as I'm within state lines? I have my MCP(California Motor Carrier Permit) and all my BIT/2290/all other permits up to date. I'm really trying to cut out my current carrier's 20% and make some more profit on my other truck. If anyone has experience with this specific situation, I would appreciate the insight! Thanks in advance.