This is a follow-up to another question. I asked "Should my readers be able to identify with the bad guy?" and got an excellent answer which explains the continuum of "identifiability" for bad guys.
In his answer, Standback also cited George R.R. Martin's "A Song of Ice and Fire" as an example of complex conflict, which was spot on: I loved those bad guys, and even wanted to re-use the idea of following one character per chapter, which I saw for the first time in Martin's books.
So my bad guy, Pio, is in the mafia, and he's after a peer of his. He's already managed to put the blame on Salvatore for something bad he's done himself, and now that Salvatore is out of jail, it's time for Pio to kill him. Pio is ruthless, macho and brutal, but I still want to take the time to explore his psychology. There are certainly reasons for his traits which are just exacerbated instances of our own "dark sides" (or at least my own, anyway.) And he's probably going to have some good moments as well - maybe he'll fall in love? Or learn a valuable lesson and feel the burn of shame for a little while?
Ultimately, though, he's still the bad guy. Is it a mistake to try to explore his psychology? What should I do or avoid in order not to spoil the main conflict of the book?