I think you are confusing a breaker group with your total residential connection. Assuming you are in Europe, and you have 2.5mm² cabling (which is the standar

I think you are confusing a breaker group with your total residential connection. Assuming you are in Europe, and you have 2.5mm² cabling (which is the standard for residential applications) then you are indeed limited to 16A per group. However, there is nothing preventing you from using multiple groups for one appliance. This is actually typical for high-power appliances, such as induction cooking. Ultimately it is your main fuse that limits your total power consumption, which for most European countries this is typically rated at 25A (5750W), but on request you can usually have this raised to 35A, 50A or even 80A, if supply is sufficient.