Originally Posted by Casilda
I remember once trying to develop a flow chart to see just how complex such an arrangement could get. It was possible to have a closed circle of six individuals, but it was also possible to have a tangled knot comparable to the Hapsburg family tree.
According to Phlox in A Night in Sickbay (season 2), his network has 720 familial relationships, 42 with sexual possibilities. I'm assuming he'd only count the people he interacts with, however, since technically all denobulans in existence could be linked to one another that way.
It seems he's also allowed to date outside of his three marriages, at least while he's away from home, as when a woman from the ship hits on him, he tells her he has three wives, but doesn't use it as a "so, you see, I can't date you" line, and is only informing her because he feels she doesn't realise the cultural gap between them.