his department is with the same university/school, then your H1 allows you to work for him. However, you can only negotiate an overload (with your department and HR to get some paperwork done) since he wanted to pay you on their payroll.
If you can't work overload and want to work under the table with that department, no way.
If you can't work overload and want to work under the table with that department, no way.