Can I have 2 H1 (1 non-profit & 1 without cap exempt)

Hi,

I am at present in OPT (ends Oct 2013). I got picked in the lottery but I have an RFE for H1-2014. I have time tille July to respond to my RFE. in the mean while I got an offer from an University and they are ready to process my H1(cap exempt).

Can I have 2 approved H1s (assuming the RFE goes through) or should i cancel 1 of them?

Yes, they can process cap-exempt H-1 for you. Both can happen in parallel. If both get approved, you will have to join either of them from the COS effective date.