Can i work on L1 Visa for few months after H1 got approved?

I am working on L1 visa for company A, and Consultancy B has applied H1 B visa for me on COS, and got approved.

To work on L1 with my current company, my mgmt asked me to visit out of US and re-enter with new I94 on L1 Visa so that i can still work on L1. My intension is to work with Current company A for few months and look for a secured job and then jump on to that.

If i re-enter US with new I94, will my approved H1 affect? in later point of time can i apply job for other company with H1?

Please suggest…thank you for help!!