My field is fluid mixers, but I suspect solid powder mixers are similar - don't bolt a bigger motor or gearbox on the assembly unless you don't mind creating a failure somewhere else. Mixing equipment is typically sized for a mechanical load and if you increase those loads, everything could fail including its mounting / support structure. That gets very dangerous.
It sounds like you appreciate a fresh approach to sizing to reach a given process outcome. If you're limited to equipment you have on-hand, or want to try your luck with used machinery, give it a go. If you want a legitimate process calculation and sizing, a mixer manufacturer should be able to collect this information (and quite a bit more) to quote you a mixer that will certainly do the job.