I am in my 9th year of H1B which is expiring on 08/31. My I-140 is approved and I-94 is valid till Feb 2011 as I entered in US using my AP in Jan 2010.

I am getting job offers from two companies but they have not filed for my H1 transfer yet.
My question is can they file for my H1 transfer even after 08/31 when my current H1 has expired, as my 1-94 will still be valid till Feb 2011 (based on my AP entry).
Also, if both the companies as well as my current employer file for my H1 can I work for any one of the three companies or do I have to join the company whose approval comes last.