Say an individual's Cartesian mind has been removed from that person (somehow). Would it be possible (in principle) for another mind to take over the "mindless hulk" of an individual?
Yes. This is a common assumption among spiritual dualists. Stephen Braude discusses it here:
Ian Stevenson, in his child past life field studies, encountered several adult drop ins: https://med.virginia.edu/perceptual-studies/wp-content/uploads/sites/267/2015/11/STE29Stevenson-1.pdf https://www.questia.com/library/journal/1G1-17935536/possession-and-exorcism-an-essay-review
And JP Moreland considers all of Stevenson's data is drop ins: https://clearlens.org/thought-snack-evidence-for-reincarnation-or-possession/