Legal Question in Civil Litigation in California

Based on just this information, it's not possible to evaluate what your lawyer says. What I can tell you is that, if he makes a counter-proposal, he will thereby reject the current proposal. It won't be available for you to accept later, and the insurer won't be required to propose those terms again. (I'm not saying it won't, but the possibility is there.)

There are any number of reasons why the insurer might refuse to offer more. For example, if its current offer reflects the insured's policy limits, the insurer won't go any higher. It's also possible that the insurer thinks your claim isn't worth as much as you think it is. Or it may just be playing hardball with you. There are other possible reasons as well.

You're free to seek a second opinion if you don't like what your lawyer is telling you. That will require detailed discussions with a second lawyer, and it beyond what this site can offer. Feel free to contact me if you like. You may instead want to contact someone closer to where you live.

Whatever you decide to do, good luck.