Like I said before, if you use your EAD, your H-1 is invalid; you are no longer H-1 worker.
You can work for 2 companies, but you are working for 2 companies with your EAD, not with your EAD and H-1.
You don't need to do anything, but your employer has to file a new I-9 to indicate that you are working on an EAD.