Given the information shown so far, Hawkmoth has only one goal: he wants power.
Specifically, he wants the power that will result from using the Ladybug and Cat Noir Miraculouses at the same time.
In his own twisted mind, he probably sees himself as making the world a better place and if he achieves his goal, he'll be able to remake the planet as he sees fit.
He even says to Ladybug and Cat Noir that they are responsible for all the destruction he is causing, because they fight back.
But unless he can wear three Miraculouses at once, he'll have to remove the Moth Miraculous, which will count as a conscious decision to give up the power and revert whatever supervillian who exists at that time, because his Akuma related powers stop functioning.
My theory is the only the earrings and the ring can be used together, because they're designed to work that way.
It wouldn't be possible to merge the Bee haircomb with the Moth brooch for example.
Or any other combination that can be made.
As regarding his status when Le Paon arrives, I think it will go something like this:
At first, they'll be equal partners.
But slowly, he'll be pushed into a supporting role and eventually end up as nothing more then her assistant.
Basically, she'll be giving all the orders and all he'll be able to do is resent his loss of dominance/authority while obeying.
A fair reward for someone who craves power, to become someone's servant.
Truthfully, I don't think Hawkmoth cares about anyone, but he does appear to have compassion sometimes.
For example, he sounds really angry about Juleka, that's he taking her misery personally for some reason.
Maybe he is the person who everyone ignores, so he takes her predicament personally.
Another reason to seek power, so that nobody can ignore his greatness?