All my campaigns are more or less villainous. I encourage my players to go hard on their characters' motivations and goal. I offer easy solutions that hurts people, solutions that put them at odds with society and its norms. One game a character released an ancient enemy of the people in order to advance their own religious doctrine. Another they sold out a band of troll hunters to the trolls for wagon loads of treasure. That event also released the troll king from its prison of chimes sparking a troll march. Final example, the campaign I'm sketching on currently will have the party be a part of a caravan expedition. Peeling back barely a layer and you'll find imperialism and colonialism motivating the existence of the caravan.

So yeah, going villainous is very doable. The thing however is to figure out what will stop the characters from just killing everyone in their way. Easiest is to make sure there are powers more powerful than them and the fear of them keeping the characters discreet. Or they have to follow some rules to keep benefits from some organisation. Or morality? Who knows it may be that the character's gran-gran disapproves of killing and the character doesn't want to upset her.

And as always - talk to your players. You as a group probably can figure out what will keep your characters in line.