This is a good idea with any hi channel AVR for more than just providing adequate audio power. Most of these AVRs are both under power supplied and under heatsinked. By added 2 or more external amps, you offload demands on both in the AVR. Less sag in the AVR PS also helps maintain performance in the remaining channels. For this, you will need an AVR with all-channel Line outs. I was serious several posts back on the $399 Onkyo TX -820. You can't beat it for $399. Has line outs, and room correction (No Audessey but it works.)
Buy from Amazon and run the heck out of it during the 30-day return window. Buy a couple older stereo amps/receivers like Yamaha AX-596 for the external amps. Cheap. (You could instead get a new as501/701 for the external amp, and still be within budget) A couple USB fans sucking up on top of the Onkyo won't hurt.
Onkyo TX-RZ820 THX-Certified 7.2-Channel 4K Network A/V Receiver
https://www.amazon.com/dp/B071VF518B/
Another suggestion: If you are using the AVRs HDMI, stay away from Any unit, all brands, that are more than about 3 years old. That way you avoid the notorious TI HDMI multiplexer chip that unsoldered itself. Almost universally used back then..
Good Luck and Enjoy!