How could monarchies and republics share an Italian federation?

How could republics and monarchies be integrated into the hypothetical Italian federation?

A monarch could serve as ceremonial head while an elected prime minister and legislature handled administration.

The constitutional follow-up asks how republics and monarchies could integrate. The proposed arrangement gives a monarch the ceremonial headship and an elected prime minister the administrative role. The monarch would retain influence while the elected institutions controlled the machinery of government. Practical power is expected to fall somewhere between those positions, without a detailed constitution being settled.