Can I have 2 H1 transfer

applications for 2 fulltime jobs? My situation is: working for companyA who is applying H1 transfer with
regular process. CompanyB gives me a better offer. Would I have to withdraw H1 for A before submitting H1 application for B? Then I would become out of status for a short period, right? Would you advise? And would INS get confused by the change of my application in such a short time? Thanx a lot!