Or put the amps in the loft/attic - that's where my setup is for whole-house audio.
Just add a volume control in each room if needed, or use voltage-controlled volume ICs between the receiver and amps, so you don't have to run long audio cables.
I'm part way through redoing my whole-house system to stereo everywhere, from the mono system I built 20 years ago when I first moved here.
Only a couple of pairs of speakers and amp inputs from the mixers are connected in at the moment as I'm still rewiring rooms, as I get time.
The amps are ebay TPA3116D2 stereo modules, modified for balanced input as I posted a few months back on here & with extra heatsinking; they work very well, using an old industrial 24V 10A supply.
The XAP800 mixers higher up in the rack are superb for multi-room setups, they have 12 inputs & 12 outputs each that can be cross-connected or controlled either by a computer serial link, or by creating preset scenes that can be selected directly by switches.
And they are often only around 20- or so on ebay, to give facilities that cost thousands in branded audio gear.
With mine, they also handle mics for voice control and echo cancellation on those so they ignore music etc.