I was working with Company A on OPT. The firm applied for an H1 for me, which got approved. I quit the firm in June 09. My OPT expired on July 7 09. I am now in my grace period which ends Sept 5 09.

I'm looking for another job since a company B can apply for a new H1 before Oct 1. Is that right? I want to stay here till atleast Sept 25 to maximise by job search chances. What happens if I overstay for 20 days? Will a new employer still be able to file for an H1 while I'm out of status? Will this seriously affect my ability to return to the US as a visitor or student?

Also, could I apply for a change to the B1 status? If yes, could I stay past Sept 5 if my application is still being processed?

Thanks.