H1B Cap to Exempt to Cap

[vipinkumarr]

I had a cap subject H1B in 2012 on which I worked for 1 year plus. Then I moved to a non-profit H1b (cap exempt) in 2013. My EB2 was filed in May 2015 and I got my I140. Since then, I am waiting for the priority date to be current (India) and renewing the H1B every three years. My current extension is valid till Nov 2021. I have a few questions:
1. Can I move to a for profit H1B now without going for a new H1B cap subject one?
2. Can the other company file my new H1B without keeping me on the payroll with the view that I will join when my new H1B is approved?
3. Do I need to go out of country to re-enter on the new H1B as I am here in USA for more than 6 years on any H1B?

[User099]

1. Yes.

2. Yes.

3. Normally you don't have to leave to extend your status. Unless your employer files extension in Consular processing. 

[gopalakrishnach]

1. Can I move to a for profit H1B now without going for a new H1B cap subject one?- I thoguht you need to go through lotter if you want to move from non-profit to profit one. I cannot answer this.
2. Can the other company file my new H1B without keeping me on the payroll with the view that I will join when my new H1B is approved? - YES. This is normal case. They will join the company after H1B is approved.

3. Do I need to go out of country to re-enter on the new H1B as I am here in USA for more than 6 years on any H1B? - To apply H1B petition no need to go out of USA. But if your H1B approval is done under consular then yes and you can come back after visa stamp.