Due to some conflict with one of my supervisor (whom i work for 20% of my salary), I am thinking about transferring my h1b to part time h1b which will cover 80% of my current salary.

There is no such thing like "Transfer of H1-B". Ther term is simply used becuased its easy to understand.
When you move to a new company, You are not transferring your current H1-B, rather you are filling new H1-B with the new company.
The only thing previous H1-B matters in the number of years completion.
You can have many H1-Bs for as many company as you want.

So going back to your question. You can easily file H1-Bs (full time or part time) with new  and still keep old as well and work in both places.

Hope this helps..