1 Terry: Cthulhu!? To deal with a bunch of space mites? This is a ridiculous case of Summon Bigger Fish!
2 Terry: Or is it the Cobra Effect, where offering a bounty on cobras leads to people breeding more cobras...?
3 Terry: Hmmm, no, it's definitely Summon Bigger Fish.
3 Steve: Crikey! Are you sayin' we should do something else?
4 Terry: Yes!
4 Steve: Breed more Cthulhus!?
4 Terry: No!!

I was looking for a trope about unintended (negative) consequences, and stumbled across the cobra effect. Which is a cool story and a neat thing, but it's kind of a bit tangential to what's actually happening here. And then it hit me:

Summon Bigger Fish is where you specifically invoke or summon a big or nasty monster to help you deal with some other monster.

Now where have I seen that before...?