You could "drop off" amperage at each floor. Do a load calculation for each floor. Let's say it came to 100A per floor.
The first panel would have a 400A MB, 400A busses and 400A feed thru lugs. The second panel could have 300A ratings for MB, busses and FT lugs. The third panel 200A and so on.
In my example, you may even be able to use the tap rules and use 300A wire and lugs between the 400A panel and the 300A panel. And so on down the chain.