H-1B transfer from profit to non-profit and back to profit after 6 years on H1B

[anonymoususer12345]

I am looking to switch jobs from a non-profit to for-profit company and not quite sure how it would work in my situation. I would really appreciate if I can get some help and insight into this.
My initial H-1B in 2009 was at a for-profit company and I was counted under the cap. I transferred to a non-profit company in 2013 (within first 6 years of H-1B) that filed my green card application and I have an approved I-140 now. 
Can I switch to a for-profit company now without being subject to the cap? Or will I be subject to the cap again since I have been at a non-profit (cap-exempt) through and beyond my 6 years of H-1B?

Thanks in advance for your help. 

Edited February 22, 2021 by anonymoususer12345