Nop.

H1-B rule says: Strictly one company [payroll] at a time. Yup it sucks that you don't have this freedom until u get your EAD or Green Card rather to be more specific. I know this is not the favorable answer but this is the reality. There has not been any reform talks yet and I don't see this rule changing anytime soon. I don't know ur situation but if u have good connection with both companies you can make them work out C2C and have only one company run your salary. There are lots of ways to get around but depends on your relationship with these companies.

GoodLuck.