3 channel 10+bit PWM
If you are flexible, use an Arduino Lenoardo, it has a high resolution timer that can drive 3 pins. 32U4, page 130, 10-bit High Speed Timer/Counter4
EDIT: it seems like analogWrite() doesn't support it

You can mimic 10/12 bit timers with an 8-Bit timer, by skipping cycles. I wouldn't know of a way to do this with the Arduino PWM library (analogWrite()), but if you are willing to handle timer interrupts, it becomes feasible.