Legal Question in Immigration Law in California

Re: Second H-1b

[Note: the following is based on information insufficient to enable reliable legal advice, and so is not intended as legal advice, but only as general guidance.]

So long as you have maintained status, you may start at Company B as soon as it files its petition for you. (You'd have to quit upon denial of that petition.) You can go to part-time for Company A as soon as it files its amended petition and new LCA.

Assuming you already have been counted against the H-1b cap (which you have been, unless your current employment is exempt), then you won't be counted again for Company B -- so no cap problem.

These employers should be offering you competent legal advice; if they're not, you must retain your own; don't assume they know what they're doing; don't risk falling out of status, having to depart for a new visa, working without authorization, etc.