H1B transferred to 2 companies simultaneously?

I am currently working for Company A under H1B visa. I've recently accepted an offer from Company B and they are now in the process of transferring the visa.

If another company, Company C, is willing to give me an offer now (I want to work for this company better), can I start working on the transfer visa to them (Company C) while another transfer (to Company B) is in process? two situations: 1. what if the transfer to Company B is just filed but not approved yet (CIS receives the application)? 2. what if the transfer to Company B is approved? Do I have the choice to go to Company C?

Thanks very much, again!

There shouldn't be a problem with applying for both transfers. There's no restriction on applying for multiple transfers at the same time.