PC: Constitutional Monarchy w/ Polygamy

By which I mean something akin to the Ottoman Sultans of Chinese Emperors, a *monarch* with multiple wives and/or concubines, with the line of succession between his sons being decided by *politics* -- in OTL history translating to palace intrigue, but TTL translating to a wider democratic political reality, with the government being based on a modern-style multiparty parliament. Is something like this possible?
 
Swaziland has a polygamist monarchy right now, and has a theoretically democratic parliament. Just make the country a real constitutional monarchy we've got what you want.
 
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