Maybe i'm wrong but i believe that Naboo (from starwars) has a system that might fit what you want to do) as in you could take inspiration from it and so on...

A more direct answer to your question, yes it's perfectly possible you could even separate the state powers and divide them between the monarchy and the political side where 1 has power over its attributes and can't interfere with the other in which case i'd suggest give the military to the monarchy as in they role in society is to defend the people(like in ancient times mostly).

Maybe I'm wrong but I believe that Naboo (from Star Wars) has a system that might fit what you want to do - as in, you could take inspiration from it.

A more direct answer to your question: yes it's perfectly possible. You could even separate the state powers and divide them between the monarchy and the political side where 1 has power over its attributes and can't interfere with the other in which case I'd suggest giving the military to the monarchy, as in, their role in society is to defend the people  (like in ancient times mostly).