Cap-Gap over STEM extension

My Current Status:My Post-OPT expires on May 31st, 2016My company A which was e-verified got acquired by company B(not e-verified)Company B is filing my H1-B under Cap-Gap. They are not planning to enroll for e-verification.1.) I am applying for STEM extension through e-verified Employer C with Start date as June 1, 2016? Will it affect my H1-B application with Employer B?2.) If my STEM application through Employer C gets approved. And, my H1-B application gets picked up in lottery in May. Can I continue working for Employer B through Cap-Gap? OR Do I need to leave employer B and work for STEM extension approved Employer C?