@CppGuy I only have a hot water heat pump and live in a hot climate, so naive. Is the system designed to heat your entire house? If it's so cold 11kW is not enough, could you only heat part of your house?
When I visited family in the UK, to save money they only set their gas oil heaters to heat a few rooms at a time.
You'll probably need 3 phase power to go above 11kW.