could I mount a different manufacturer brand rotor to use with my brakes?
The brand of brake doesn't matter. The only variables you should care about are:


Rotor diameter. You should probably get the same size as the old one; for a different size, you'll need an adapter to reposition the brake calipers.
The way the rotor attaches to the hub. Most of them are held on with 6 bolts, but a few use the "Centerlock" attachement which looks like this: