Can I transfer my L1A

I am currently working in the US on an L1A visa. We have started the green card process and I am being told that within 60-90 days my EAD and Advance parole documents will be provided. There is then an estimated 8-12 month administrative delay until final processing and I receive lawful permanent residency status.

I have received an offer from another company in the US.

Is there anyway I can work for another company immediately under and L1A and while I wait for my EAD? If I receive my EAD in 60-90 days can I then go and work for another company or I do I have to wait until I receive my lawful permanent residency?

No, your L1A is for the company related to the one you worked for outside US. It is never transferable. You would need a TN or H1 in the meantime, until EAD is in hand.

Besides, your GC process (assuming it is thru your company) may be pulled if you do not stick it out at least 6 months after filing I-485. So, merely having the EAD will not allow you to leave your sponsor.