H1 to L1A to H1

[kka1]

Hi,

I had a COS from H1 to L1A and currently have around 2+ years for the 7 year term to complete.

Green card filing is not yet started by my employer and not sure when it will. 

So, my questions are -

1. Can I go back to H1 (COS from L1A back to H1, in which case, I will have 1+ year left) and get PERM filed from a new employer before max out of H1, that is before 365 days of my H1 end date (after COS to H1)?

2. Can a new employer apply for COS from L1A to H1 as I was on H1 before and there is still term left? 

Looking for responses and suggestions.

Thanks a lot in advance!