Exactly, a "cooking fuse" is not uncommon, which is two 16A lines to the same stove. That gives you 7360W to play with, something you won't reach in practice.
Alternatively, if you already have a multi-phase connection, then you would of course have the lines on different phases. If you have a 3-phase connection 25A main fuse is common, for single phase connections 35A is common.
Just to clarify here: when you talk about a "main fuse", you mean one that sits between the meter and the entire rest of the panel, correct? So individual circuits would be downstream of the main switch.
For context, most American homes have 240V split phase (single phase for all intents and purposes) service with a 200A main breaker.
Wtf do residential homes need 48 kW of power for? I guess it's nice to charge your car quickly, but other than that I'm struggling to think of any uses.
Simultaneously washing and drying clothes while cooking a turkey in the oven, brussel sprouts in the toaster-oven, boiling water for tea, distracting the children with a computer or tv, doing some welding in the garage, and powering a bunch of Christmas lights. --- This is something that actually happened one year. It is much easier to use a big wire and a big breaker/fuse to the house than to have the power go out.
Between my electric heat, dryer, stove, water heater, and car it's easy to get close to the limit, and that's before anything that runs on 120, like computers, a refrigerator, lights, or washer.
Three phase on the other hand is a slight of hand, since that gives you more power than what 230V would imply ;)