It would take one hell of an author to pull off what you are asking. In character, Ranma isn't likely to try for multiple relationships like that; He's too damn shy to say his own feelings most of the time and the one time he thinks he's being propositioned for sex (as opposed to a date or hug), he stammers, blushes... I don't see him trying to be intimate with even one person for quite some time after the series ended. Without the assist of a deus ex machina.
The Tendo sisters, meanwhile, would not want to knowingly all be involved with the same person. Kasumi would think such a relationship is improper. While Akane is the type to get jealous rather easily. You really think that she'd willingly share Ranma with anyone? Much less her own sisters? I think not. Nabiki is interesting, because while she'd probably not go for it the main thing that would prevent this from happening would be Ranma's full awareness that she'd threaten to reveal the relationship to everybody.
The other possibility is that they're sharing him completely unaware of the relationship each other has. This is equally likely to fail. For the sake of argument, let's say that Ranma secretly has a relationship with each of them. As stated above, Nabiki would blackmail the hell out of Ranma. Kasumi would probably not want to keep their relationship secret, out of respect for her family. Akane would... probably be okay with the idea of keeping it secret, but utterly fail to do so. Meanwhile, Ranma would be very much unable to keep the whole thing secret because he's like that.
Essentially, no matter how I look at it that sort of fic would be very hard to pull off. I'd say impossible, but then someone will go ahead and post something to prove me wrong.