Concurrent followed by Amendment for H-1 with a new employer

[sam7dent]

current scenario is -

Currently working for company A - full time H-1 will be maintained till May 12 and then we are terminating the relation mutually.

Now if a Company B is ready to offer me a part time H-1 till May 31 and then convert to full time.

Questions:

1. Can company B file a part time Concurrent H-1 B petition as "extension of status" so I can maintain a Full time H-1 with Company A and simultaneously do Part time H-1 with Company B till May 12th ?

2. If the answer is yes for 1. Then what happens to my status between May 12 to June 1st (June 1st is when the company B is ready to file an Amendment H-1 B full time to get a complete transfer of employer from Company A ) ?

3. Kindly, suggest if the above scenario is feasible and if there is any risk of taking this route ? In case of any risk then I would like to start the full time H-1 with Company B after May 12th when Company A terminates my H-1 status.

Your time and advice will be appreciated.

Sam.