I'm on H1b visa in my 6th year. Perm application has been filed and I hope to get it approved soon along with approved i-140 (fingers crossed).

From what I have read on this forum so far, H1b transfer to a new job after an approved I-140 seems to be possible even after 6 years on H1. My issue is that I currently work for a university (non-quota H1) so if I get a new job most likely it will be with a for profit company which would require me to get a new H1 (and not H1 transfer).

So, the question is whether it is possible to get a new H1 after 6 years on H1?

Thanks for any help.