Sure. Why not? You wrote that it would be "(republican)".
What if say California were to adopt a (republican) parliamentary system? Like say, where the governor is elected, but he/she is powerless and just appoints a cabinet from the majority party or coalition in the legislature, and dissolves the legislature on the advice of the state's prime minister and calls for new elections? And of course where the legislature would have a maximum amount of time it could serve?
I wonder if that would be constitutional.
