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

[uday029]

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?

Thanks.

Less

[inadmissible]

Company B can contract to supply services to Company A