Can i apply New H-1B Cap Exempt while CAP H1B is in process for same client

I am working as a contractor (‘A’ Company Non profit) I have filed H1B through CAP 2021 it got selected by lottery Recently (‘A’ Company Non profit) they gave full time job offer and they are willing to apply through (New H-1B Cap Exempt)


1.Can i apply for Non profit H1B (Cap Exempt) while H1B Profit (CAP) is the process for same client