Any house rule is possible, but it certainly wouldn't be the norm. More to the point though, I don't really understand why you'd want to.
If you're worried about the dealer cheating by stacking the deck to deal themselves a certain card/cards, in most cases they'll be putting that card either on the top or bottom of the deck, which they'll then give to themselves either by dealing to themselves from the bottom or dealing seconds to everyone else then taking the top card themselves.
So - assuming the other person is performing a fair cut, the cards on the top and bottom should still be randomised and it'll serve pretty much the same function as completely reshuffling the deck.
Also, a full reshuffle would take up time unnecessarily, making you (rightly) incredibly unpopular with the rest of the players at the table.
Use a cut card, perform a fair cut, and just don't play in games with anyone you think is still capable of stacking a deck or cheating even after you've taken those precautions. I'd be an awful lot more concerned about card marking or collusion (neither of which would be prevented by having an independent reshuffle) than I would be about deck stacking.