It took me a while to realize that some of the weapons can combine the primary and secondary firing modes into a third one. The painkiller can shoot spinning blades (which sucks because it does fucking nothing unless hitting the target dead-center despite the projectile being huge), the stake gun can launch its grenades farther by hitting them in mid-air with a stake (which is more of a combo than a third firing mode and actually requires some skill), and the shuriken/lightning gun can shoot this electrified mine thing (which actually makes the weapon viable).
According to the Painkiller wiki which I refuse to browse any further because Fandom is garbage, the chaingun/rocket launcher can detonate its rockets in mid-air with bullets, but I don't think I've ever tried this. It also claims the shotgun's """combo""" is freezing enemies with the secondary fire and then finishing them off with the primary fire, but I call bullshit because it's the natural way to use the secondary fire (unless your instinct is to walk away and let them unfreeze), so it hardly counts as a combo.