Over the years I've used guitar and bass multieffects to process drums. Might sound like a mismatch, but wah, delay and reverb, distortion, overdrive, Eq, compression, chorus and flanger all bring life to a drum machine.
The cheaper the better (we are not looking for genuine cab Sims) for the sound AND the wallet. Used a few of the Boss ME series, like this ME20B, made for bass. Works fine for drums