Changing Employers while Visa Extension is in process

[SPI]

I am currently working in company A. My current H1B expires on Oct 1 and Company A in New York has applied for an extension on May 23, 2014 in regular processing. I have not received my receipt yet. In the meantime, I have an offer from Company B in Texas that is now going to apply for my visa transfer under premium processing. Is this going to be an issue since they want me to start in the next 6 weeks. Please let me know! thanks a lot for all the help.....