Okay this is a complicated one, so I am unsure whether it works and might need some deep diving into text, but I'm curious what people think.
If your sorcerer-paladin has Booming Blade (or Green-Flame Blade) you can smite with it, as a melee weapon attack is part of the spell.
If you use the metamagic 'empowered spell' you can reroll the damage dice of a spell up to your charisma modifier
What I want to know is whether smite damage counts here?
I am already fairly certain that the weapon damage and the extra d8s at higher levels can all be empowered, because the attack is part of the booming blade spell. In other words the attack's damage dice are icluded in the spell's damage dice. (You may disagree, but I'm running under that assumption)
But what about the smite damage? That is usually doubled on a crit along with all the other dice, as it counts as part of the attack's damage dice. So if the smite damage dice are part of the attack's damage dice and the attack's damage dice are included in the spell's damage dice, then by extension wouldn't the smite damage dice be part of the spell's damage dice?