Legal Question in Intellectual Property in California

Don't think you have a legal issue, per se. This is more of a "how much do you like your paralegal job" issue. Best thing to do is ask your employer if this is okay, and if you think that's a bad idea, then you have already answered the "how much do you like your paralegal job" issue.

If you are full time, the firm may prohibit outside work, particularly in the same field. Paralegals can cread conflicts that cost the firm a big client or case. Consider asking if the firm will convert you to contractor status and then just make the firm one of your "clients" among other firms.

There is case law showing serious conflicts arising between law firms due to paralegals; I can't remember the specifics but at least one case may have involved a well-known Marin County mass-torts firm. There may be no actual conflict at present, but the possibility of one arising in the future is sufficient reason, in my opinion, to avoid working for two firms, one as an employee, without full prior disclosure to both firms.