it's actually very common on race cars to use different compounds for front and rear, depending on the car setup. When you get into the the brembo/wilwood/stoptec type of calipers, they use off the shelf racing pads which are usually cheaper than a specialized pad for a production car. You can get 4 or 5 different compounds for each caliper model, each one with a slightly different friction coefficient, for exactly this purpose.
If you want to or have to run the stock calipers about the only way to adjust the bias is with a different rear pad. On Porsches I used to go through 2 sets of fronts for every set of rears.
As with anything is always possible to screw it up.