What you are looking for is really pretty much outside what the rules can handle without major modifications. Basically this would be playing a gestalt character, and unless everyone has gestalt characters, it would be pretty unbalancing.
However, I think you could achieve the flavor of what you want pretty easy. If your second head is pretty much just cosmetic (i.e. it has no effect on the stats of you character but you can give it a different personality, its own flavor etc.) then this can work out.
I would go with a qinggong monk. You play it as though at the physical stuff is controlled by one head, but the ki stuff is controlled by the other head. Depending on what sort of thing you want to do, and what sort of actions that takes, you can roleplay which head is controlling the body, but mechanically it isn't any different than any other qinggong monk.
Play a Medium. The heads take turns on a day-by-day basis, with each head being an expert in three of the six areas. There's a feat that allows getting a different feat for each spirit. Alternatively, the Spirit Dancer archetype allows rapid shifting for midday changes. Champion spirit gets bonuses that are pretty solid, so you can take Catch Offguard and make improvised weapons work well.
Play a Vigilante, and ignore the secret identity part. Then one side handles combat, while the other is charming in social situations (or perhaps is a shrewd merchant instead). This even allows for two different alignments. Fist of the Avenger makes using unarmed strikes not bad.
Unless this is being played by two players, then you should probably figure out how to use existing rules to accomplish your goal instead of getting a stronger, more versatile character than all the other players.
Worth noting, a tumor familiar (or aberrant tumor) does allow you to essentially have two characters in the same body. Sage archetype on it for decent mental scores and separate skill points, and a Tiefling with GM permission to use the variant ability for contact-only telepathy, and bam- two characters, one body.
The character was supposed to be played by two different people at the same time. But I do realise it's probably a lot more complicated than it's worth..
I guess I'll try to make it work as one of your suggestions ;) I'm giving it a look right now!
If it's two people, then that's much easier- you're balancing against two characters instead of one. Ratfolk can occupy the same square together with the swarming racial trait, so you could probably build a pair of Ratfolk that always move together, then ask your GM for modifications from there to fit your needs. (Change to one medium size body, but can't two-hand weapons, must take same physical stats, and use lower for AC/CMD, both roll and take worse for reflex and fort, but pool hp and non-mental single-target buffs apply to both.)
