1. The answer is No. There is no advantage in going through for-profit or non-profit that's just irrelevant.
2. No, non-profit or for-profit does not matter you cannot transfer I-140s, you can transfer priority dates unless your 1-140 is based upon a National Interest Waiver or an EB-1A. Your green card can be transferred once your I-140 is approved and I-485 has been pending 180 days, then it doesn't matter what the nature of the organisation is.
3. a. I don't think there is any specific law on this issue. Technically, you can start working for them on receipt, but obviously you will only get a receipt if your case is picked up for the lottery. So if you have been maintaining H-1B status I believe you can start working for a cap subject employer as soon as your H-1 is picked up.
b. Absolutely. My guess would be if your H-1B cap subject H-1B is approved and it is not revoked till October 1st, I don't think you will be subject to a cap to work for a for-profit in the future. It shouldn't be revoked before October 1st and you should receive your change of employer. So in other words, you should get a new I-94 with the case because USCIS has been taking this position that just getting an H-1B approval does not put you over the top where you are safe from cap quota issues. They say unless you receive a change of status or go get a visa stamping till that time you are not exempt from the quota so you must also receive an I-94 which is a transfer of employer, but you can still continue working with the old employer.
c. Another way is applying for concurrent H-1B although it is a strange provision in the law where if you have a quota exempt H-1B as long as you maintain that without worrying about the quota you can also work on a concurrent H-1B for a quota employer.
d. Moving to H-4 EAD is not a good idea because in June they are going to announce the revocation of the H-4 EAD regulations according to the court.
e. Joining a Master's CPT and filing a cap yes, that's definitely an option.
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