Sure, you would be able to put smaller power draw items on the same circuit, but between the CPU/GPU/Motherboard/PSU/Monitors/Peripherals you will not be able to put two of these machines onto the same circuit.
Maximum available power for standard domestic users is still only 3kW in many places. Might not be enough for a gaming PC, washing machine and microwave!
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.