Is it legal to work for two employers (one full time, other part time) on H1B?

I am currently working full-time for Company A (have H1B and approved i-140 with this firm) and have very good work relationship with them. I recently accepted another full-time job with Company B and they have applied for H1B transfer. However, my current employer (Company A) asked me if I can work part-time (variable hours each weak) until they can find my replacement which could take 6-8 months.
Is there a legal way for me to work full-time for Company B and concurrently work part-time for my current Company A?


H-1B services are not transferable. Only one employer has right of access to you at a given time. However, a legal option that is workable is for Company B to pay you for your services to Company A. Some companies work on this model, others find it too confusing.