H-1 is only supposed to work for the firm that sponsors his h-1, My saying is H-1 can part-time work for other firm as long as he/she maitain his H-1 status, which means full-time working for his employer.
This explaination is on former INS memo, so that is one thing for sure.
I guess that's why some lawyers believe that H-4 can use EAD to work while not losing their H-4 status. In fact, my lawyer's some clients do this thing, It's no problem for them. I have to say on this issue, there is no rule clearly say can or cannot.
hopefully, that will help
