If you can get power from the neighbour or a generator then you will have the ability to keep everything running. IMO, I would try to keep it in full operation, as then there won't be any shock to the tank.
If you don't have that option and have limited power, like a battery backup, I would keep movement of the water column, so you need to keep some powerheads going... The heater and return pump will zap a battery, so that isn't an option. With what you stated, I would keep the 2X MP40W going, worst case just one.
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Setup: 180G DT, 105G Refuge (approx. 300lbs LR, 150lbs Aragonite)
Hardware: Super Reef Octopus SSS-3000, Tunze ATO, Mag 18 return, 2x MP40W, 2X Koralia 4's Wavemaker
Lighting: 5ft Hamilton Belize Sun (2x250W MH, 2X80W T5HO)
Type of Aquarium: mixed reef (SPS & LPS) with fish
Dosing: Mg, Ca, Alk
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