How could we get, in the 19th Century, an arrangment where France had a monarch with at least some real powers, but the monarchy was elective/selective and was picked periodically from among a Bourbon candidate, an Orleans candidate, and a Napoleonic candidate. Perhaps each of those three factions could have their own distinct method for choosing their candidate (e.g., the Bourbons, strict hereditary? The Orleanists, universal manhood suffrage?)