You don't say whether it's airline, corporate, GA, or whatever. You can certainly request more money, but I wouldn't expect a positive outcome unless there's a requirement to have both licences at the same time on the operation (tiltrotor is the only case I know of), or they can avoid hiring an additional pilot because of the skills you have.
If you're going to be flying tiltrotor, I doubt you'd need us to give you advice on salaries. If they can avoid hiring an additional pilot, then I'd ask for a percentage of the salary they saved.
My expectation would be to be paid for whichever licence gives the highest salary, but don't let me stop you asking for more ...
(Yes, I do fly both)