USB power negotiation

Hello All,

could someone more experienced with USB help me please?
We would like to power a BeagleBone Black with the default Angstrom linux image solely over USB. We did a measurement, showing that the BBB eats c.a. 150mA not doing anything, and 360mA with a benchmarking program running. USB2.0 can provide us 500mA.
We fear, that when we connect our peripherals, the 500mA-s would not be enough. Is there any way to use the device from a USB3.0 port (or USB3.0 power) and negotiate for more power, e.g. 6-700mA? We can only use a single USB port, so power cables are not an option.

Thanks for the help in advance,