The two systems that would be best suited for something like this (that come to my mind anyway) are Pathfinder and Shadowrun.
Pathfinder is your typical high-fantasy role playing game inspired by Dungeons and Dragons (3.5 edition, specifically). This opens up the possibility of magic and potions as a means of these forced transformations. It also opens up a vast multitude of fantasy races for your players to choose from (each with their own racial bonuses and/or penalties). This is your standard D20 based system in which your players would require a full set of dice ranging from the lowly D4 all of the way up through the D20. A D100 might also help, but is hardly necessary for anyone except yourself. Of course, they could also opt for some form of online number randomize if your players are not usually tabletop gamers and do not have a full set of dice.
Shadowrun, on the other hand, is a futuristic fantasy-themed cyber-punk system based entirely around the almighty D6. All that your players would need is a handful of D6 dice, which can easily be raided from any board games that they might have laying around. This system contains magic, hyper-advanced technologies (from cyber-implants to gene splicing), and a rich lore based in our own world. There isn't much that a creative game master cannot do in Shadowrun.
Both of these systems offer systems of character interactions that can be as simple or complex as your game might need, based on your own discretion as game master. Shadowrun is the far more complex system, though, despite the fact that it relies solely on D6 dice. They both also offer combat systems should you wish to incorporate fighting into your game. As with the social features of the two systems, Shadowrun offers the more complex system. Actually, if we are talking combat then Shadowrun is pretty advanced.
Both systems can be altered to suit your needs, of course. Role playing systems are meant to serve only as a guideline for the game master. It is up to the game master to decide when to alter a rule or to get rid of it altogether in the interest of fun and fair play. Any role playing book worth the paper that it is printed on will tell you that in the first few pages.
Anyway, I would advise looking into Pathfinder and Shadowrun, depending on the kind of role play that you were going for. One is your typical high-fantasy and the other is futuristic cyber-punk.