Transferring companies when on H1B Receipt Number


I am currently working for a Company A. Company B has started my H1B Transfer process and is yet to get a receipt number. Now Company C has expressed interest in hiring me but I can only give the receipt number/I-797 for the Company A to start my H1B Transfer. So if I join Company B on receipt number and then Company C gets my receipt number, can I join Company C? Company C is doing my H1B Transfer based on receipt number/I-797 of Company A.

Will this affect anything, like Green Card, etc.?

Thank you