H1B profit to on-profit to profit orgainzation

USA H1B Visa
1

Hi All,
I am currently offered a job at a non-profit and I already have H1B subjected to CAP. If I join the non-profit now, would I be able to move from non-profilt to profit later again ? If yes, is ther a time limit on it ? Also, they promised me Green card processing, would I be able to move from non-profit to profit after my I-140 approval ?

Thanks in advance!