2 Job offers- 2 prospective H1B's

[p-desh]

Hi,

 

I am working  on H1B for staffing company A (forprofit). I got a job offer from company B(non profit org.)they  transferred my H1b to their org. I haven't started for them yet.

In the meanwhile I received new offer for Company C (for profit-through my original staffing company A)

My  questions are - can my visa can be transferred to employer C at the same time and I will be holding two visas if company C visa approved.

 

Can company B can sue me for  transfering  my visa(and paid for visa expenses)

Kindly suggest- Regards