Not sure more voltage will give more headroom to a pedal that clips the signal with diodes... You probably are not getting op-amp clipping with a normal tube screamer, so it is unlikely the higher voltage will change anything at all.
If you want to build a OD circuit that has a higher output, that is a different question. Higher threshold clippers (LEDs? Series of diodes?), maybe a booster after, maybe changing the gain of the second opamp stage (makes things shrill if you don't adjust the tone control somehow.) None of these require higher voltage, but then you might see the benefit.
You would change all connections to ground to -15, all connections to +9 to +15, all connections to Bias voltage to 0v. You are biasing two transistors and two opamp stages.