Most people aren't willing to 3-barrel draws or in general at these stakes, so I might lean towards folding. If they were on a draw, they'd probably check back the turn, and almost always they give up on the river when our hand is pretty much face-up to a K or overpair.
Also not happy calling the river with that bet sizing. Min-raise flop, half-pot, bomb river. When their bet sizing changes suddenly, even when their line makes no sense, it's generally a strong hand that missed value OTF/OTT and is trying to maximize value OTR.
We can probably also find an exploitable fold multi-way. I expect to see sets, top two, and big combo draws here. He's not bluffing here multiway with the BB to act behind here, and against that range, we have really terrible equity. I think sets and top two are going to make up the majority of his range here though. I don't remember seeing aggression with big combo draws until 50NL; even then, the flop/turn raising aggression with them is minimal.