I have a microwave (1270W) and dishwasher (2400W) on the same circuit (230V, 16A). It didn't trip yet...
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.
For context, most American homes have 240V split phase (single phase for all intents and purposes) service with a 200A main breaker.
Three phase on the other hand is a slight of hand, since that gives you more power than what 230V would imply ;)
3kW is typical kitchen power.
> 3kW is typical kitchen power
Most stoves used to be gas powered. Now induction is becoming more common (but it requires an upgrade to 4.5kW).