Make aspects have ongoing effects.

There are already rules for how to make there be ongoing damage. Aspects are always true which means that they can have lots of effects. They can cause damage, they can impede movement, they can block line of sight, they can make checks harder, they can do lots of things.

For example, if someone throws a motovolmotolov, and sets the zone on fire, if you don't move, you could get burn damage because the room is on fire. You might be unable to see stuff because there's smoke. It's gonna be harder to do anything that involves touch, because everything is on fire, and if everyone just piles on advantages you'll all burn to death.

I've found in my games that it's easy to use NPCs to break people out of boring aspects. They do interesting things, and I give them larger bonuses for it, and tell players I'll likewise give them bonuses if they do interesting things. I might say give one damage per round to an amusing aspect someone makes, or two damage per round to an amusing one that works well with an existing scene aspect.

Make the scene or an organization a character

The bronze rule of fate is that anything can be a character. and so, it often helps in combat if you make the scene or the organization around you a character. This gives some extra narrative weight to what you can do as GM, and lets you up the stakes of the fight.

For example, while the PCs whale on Dr Doom, the Doomstitute character might send a pair of mooks to retrieve the Device of Doom. If the PCs focus on taking down Dr Doom, they might endanger the world. You can also have the Doomstitute just shoot several of the PCs with snipers, doing some ongoing damage.

These two things should let you make fights more impactful and damaging.