H1B Visa Transfer with a second employer when the first one is already in progress

My H1B visa transfer with Employer A is already in progress on a regular processing and it is pending with USCIS for the final decision. In the meantime, I have got another job offer with Employer B who is willing to do my H1B transfer on a premium processing. Is this feasible that Employer B could initiate the H1B transfer right now when the H1B transfer with Employer A is in progress ?

Yes since really there is no such thing as an H1 transfer and these are all new applications. Obviously you can only work at one place at a time.

I have started working for the Employer A. Does that change anything ?