Yes, it´s possible.
As you say, it´s not the "classical" move, but honestly there is huge variety of things that people do after MBB.
A usual way to do such changes is to actually do an MBA, many people leverage it for career-movements. However, I am not saying it´s the way, the MBA needs to align with your value proposition in multiple ways in order to go for it -it´s too much of a cost and time investment-.
Hope it helps!