qustion about part time h-1b

I work in the university right now with h1b and got a offer from a company. I can't transfer since there is no quota this year but the company's lawer said they can sponsor a part time h-1b for me and there is no quota limit on part time h-1b so I can start work for them. I can keep my current h-1b and job. Is that true that part time h1b is not subject to quota? Thanks