The H-1B petition belongs to the employer not you. There is no reason why the employer cannot file a response to the RFE. You should not face any immigration consequences from pursuing multiple H-1B petitions so long as you do not commit fraud or misrepresentation. You will eventually need to pick one employer to go with unless the H-1B petitions are for part-time work.
Answered on Aug 16th, 2016 at 2:51 PM