The EG4 / 1812 manual says you can stack up to 10 to get to 120KW. That would be 500A/240V, s 8 would get you to 400A. You'd probably have to carpet a square mile of property with solar panels and find a place to put in 8-16 racks of batteries, but you could do it. Generally the battery is about time, but if you are actually going to get a 400A demand, your going to need significant engineering, as you may need to draw around 2000A/50v from your batteries at any given point.
At higher wattage, you might want high voltage battery (400V or 1000V). Most I've seen listed are 3-phase, 230/400Y or 277/480Y.
SMA sells one in Europe that is 75kW. In the US I only see multi-MW models from them.
The problem with the EG4's is if you lose an inverter the whole system shuts down. Anybody have any experience with parallel Sol-Ark or other brands that don't fall over if you shut one off?
Sunny Island is 120V, 6kW and can be connected all in parallel, or parallel/series for 120/240V split-phase.
It will continue operating with some disconnected.
Three can be connected for 120/208Y 3-phase (18kW), and optional whether it shuts off for lost phase or continues operating.
Four of those can be connected as "multi-cluster" for 72kW.
If OP can get by with about 100A 240V steady-state, surge to 200A for a couple seconds, then stacked inverters with 48V battery should work.
But as noted by others, it is more likely to have steady state loads of a couple kW, or whatever A/C draws.
What gets tough is providing enough battery for 24/7 A/C. If A/C is only needed when there is direct sunshine, easy enough to power with PV panels. Small battery for other loads at night. That's what I have.