I would say multiple units. I don't know what the power requirement is, but 6 will be stretching it too much. Where I'm living 5-6 amps is the supply. So I try to split everything into different outlets as much as possible. This reduces the chance of over heating at the power outlet.

For matching this load one will probably need a setup with a large battery(s). You will have to manage it separately. Consider one unit setup only if you are planning to install a dedicated power setup, instead of just connecting to a power socket on the wall.

In Europe, we can handle 32A on a single plug, so I just use a powerstrip with the C14 connector, to extend my UPS.

I'm nowhere near pulling that, so I'm safe. I'm at ~3A continiously, so I have litterally no reason to worry. Plus all the powerstrips are in spec for the country I'm in, so that's another 'yay I'm good' thing.