802.3at Type 2 POE limits the current to 600ma per "mode" (pair of pairs) which is equivilent to 300ma per core.
So if you assume the IEEE got it right then you can safely deliver about 900ma on a setup with three positive wires and three negative wires. I expect the IEEE were pretty conservative to allow for less than ideal installation methods and that with a single cable in free air you could go somewhat higher.
However that is not the whole story. As Sphero points out in a 5V system volt drop is likely to become an issue before cable rating does. He came up with a current of 440ma for a 10m length and a somewhat reasonable volt drop.
An obvious solution to this is to use a higher voltage supply and then step it down at the remote end. However this brings issues of it's own. It's not such an issue for "ghetto PoE" type systems because Ethernet is isolated but the fact that you are using three wires for power (leaving one pair for data) makes me suspect that you are not planning to use Ethernet.
If you have a common ground for data and power interconnection and you raise the power supply voltage significantly above the signal voltage then you need to think very carefully about the impact of volt drop in the ground lead and also the impact of fault conditions where the ground is disconnected while the power and data lines remain connected.