H1B Transfer without Stamping, waiting for PA date

I am working for a big IT major in India who have filed my H1b, my H1b petition has been approved and I am still waiting for the stamping to happen. If I apply for a new company at this point of time, be it an Indian MNC or a US organization and get selected, would they be able to do the H1b transfer at this point of time ?

Yes, the change of employer petition (aka transfer) can be applied while your H1B is still valid.