That is actually a pretty neat module. Not sure i would trust using it at anywhere near its max power rating since i had chinese crap blow up well before the max ratings. When such a high power inverter blows up, it can be pretty spectacular with a bang, smoke, sparks, fire etc.
By the looks of it this is basically a really big open loop D Class audio amplifier. That in itself is just a pair of buck switchmode converters with an agile output voltage. So this setup will not be able to boost voltage, So the DC input determines the largest peak to peak AC signal it can make (minus some headroom for losses). So for making 220V AC it should need about >340V DC of input.
The encouraging thing is that is does have an adjustment pot to tune the output voltage, but it is not closed loop, so even if you do tweak it to make the right output voltage, it will still ride up and down with any variations in input voltage. But i suppose it wouldn't be too hard to add some circuitry to make it actually sense the input voltage.
I suppose the only thing that determines the max output power is the power transistors and output choke. So the same PWM driver module could be used to build a bigger model for say 10kW. Also since you are from the US you will need a way to get split phase in order to run a house. So you either need an inverter capable of that, or use a large transformer to provide the center tap for the 'neutral'. For EU houses its easier since even tho there is often 3 phase, we typically don't need it to actually be 3 phase in residential houses, so all 3 phases could simply be powered from 1 phase.