Two pairs of speakers on one amplifier: what the parallel load really does
Two 8 Ω pairs in parallel are 4 Ω on paper and 2.2 Ω at the dip. The Fosi V3 is rated for that; a receiver rated 6 Ω is out of spec by nearly a factor of three.
Only if the amplifier is rated for half the impedance — which the Fosi V3 is and most receivers are not.
Two pairs of 8 Ω speakers wired in parallel present 4 Ω. That is the number on the box; the number that decides the outcome is the dip. The RP-600M II's 4.4 Ω minimum becomes 2.2 Ω. The Fosi V3 is rated down to 2 Ω, so it survives. The Denon AVR-S570BT, rated 6 Ω minimum, is out of spec by nearly a factor of three; the Yamaha RX-V4A, rated 4 Ω, still is.
Current is the whole story. At 45 W the amplifier pushes 3.2 A into 4.4 Ω and 4.5 A into 2.2 Ω for the same voltage swing. A minimum impedance rating is a current limit written in the units of impedance — that is why it does not scale with the watt figure on the front panel.
The surprise: the level cost is zero here. The Fosi delivers 45 W into 8 Ω and 90 W into 4 Ω, so each pair still receives 45 W. That doubling is exactly what a receiver with a shared power supply cannot do, and it is why the A+B switch behaves at low volume and trips protection at a party.
If your amplifier is not rated for it: run the pairs one at a time, or use a switch box with series resistors and accept the level loss it costs.