You can pull the 260 and test, then use the 260's psu leads for the 470 and test, then swap PCIe power connectors around . . . checking to see if you've overloaded a rail or have a bad rail.
You may see a small voltage drop from a loaded wall outlet (can check with a voltmeter or it may show on your UPS if you have one) that might trigger one of your psu's protection circuits to shut down. A long extension cord can help you test that too
Other than that, your psu should pull as much power as it needs until the wall circuit breaker says "enough".