Steve, welcome. The source of the problem is unlikely to be either the speaker wire or the receiver. Yes, try adding one speaker at a time to see when it shuts down. This isn't looking for a bad wire, but a bad speaker with an internal short which is causing the shutdown. The "check speaker wire" warning could just as well be "check for any short", since the receiver would react to a short in one of the speakers in the same way that it would to a short in the external connecting wires.

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Enjoy the music, not the equipment.