Rats + +X tokens
Well, this at least satisfies one of the thread's qualifiers. There are a couple combos with a 3rd card/event/landmark that would probably be good in the (admittedly rare) case that you see them.
1. Rats + Pathfinding + Fortress: Having a deck with 20 labs is great. Having a deck with 20 labs and nothing else is not so great. If you can have a fortress in hand whenever you play a rats, you can keep your other cards.
2. Rats + Training + Dominate: A deck consisting of at least 14 trained rats and nothing else can buy dominate every turn. You'll have to trash the province, but still, 9 points a turn might be good enough.
3. Rats + Seaway + Ruins: Suppose your opponents has avoided rats (because there's no other trashing and they're terrible). Suppose you've drawn your deck and for some reason have at least 2 seawayed rats in hand. You can now autopile the rats and have at least 20 buys to buy out the curses and ruins and empty 3 piles in one turn. Best of all, it only costs you 10 points plus however many more you had in your hand!
3. Rats + Seaway + Tomb: Seaway rats and get as many of them as possible. Once you have <5 non-rats cards in your deck, buy enough coppers each turn so that you have 5 non-rats cards for next turn. Trashing those 5 cards yields 5 points a turn, which is admittedly less than province a turn, but (like some golden decks) is fast enough that it can still be good. On average, after n turns, you should have roughly 5n-28 points from tomb. This gets you to the equivalent of 4 provinces in 11 turns.
I'm not sure if there's much else good you can do with a deck full of rats, but there's 20 of them and you can get them real quick, so it seems like anything good you can find to do would be pretty fast.