H1B question (open my own company)

I got a question that's a little strange and hope someone could help to shed some light on it.

Can I open my own company as an H1B holder and have my company sponsor my own H1B (part-time)? Is there any requirement to the company? I heard it's doable. Not sure how true that is. I am holding a full-time H1B right now. Will this full-time H1B affect my part-time H1B in any way? e.g. Does it matter if my full-time H1B is for-profit or not-for-profit?

Thanks for your help!

p.s. pjiang: My friend told me you are very knowledgeable on the immigration topics. Can you give me some advice as well?