Since two weeks have passed with no answer for Gumshoe One-to-One, I can offer experience of doing this with a different game system. This was a deliberate experiment in having three players (the whole group) share control of a single character, and the game system was chosen to support that.
I used Amber Diceless Roleplaying, because all the players were familiar with the stories, Amberites are reasonably robust, and the background works for single characters doing difficult things.
I left it to the players to decide how to divide up control. I would take instructions for physical action from any of them if they were clear and definite, but it ended up with one player telling me most of the character's actions.
There was some confusion at first as they tried to find a structure for talking to each other. I'd expect that to be the case for any group of players on their first try with this style of play. To avoid that causing a disaster, don't start play in a dangerous situation. Also, pick players who are grown-ups, and reasonably flexible role-players. Players who always play ninjas, or have other specific preoccupations, are not likely to handle this kind of play well.
After a while, they settled into playing different facets of the character's personality. They were being, approximately, the Freudian id, ego and superego. I'm not sure if this pattern will repeat with other groups, since I only tried this experiment once, for about 4 game sessions.
They also engaged in a lot of deliberate surrealism, because Amber makes that easy, and because they felt that I, as GM, should also have a mentally taxing time. I think this emerged from surrealism being something their senses of humour had in common.
Overall, try this in a spirit of experiment, and don't assume that it will immediately lead to a wonderful new roleplaying experience. It was interesting to run, but I haven't felt motivated to try it again.