Funniest 8080-era multitasker was made by Siemens in 1976. Instead of allocating memory from common RAM, they just switched small RAMs mechanically. You only needed to dump registers at each switch. Particularly economical in 8080 which is not good for indexed memory models like Z80.
"mechanically" with relays or something? Do you know the model number?
RAM chips usually have a "chip enable" pin, you might have chips that have 4k of addresses that are 8 bits wide [1] and fill out the 64k address space by having 16 RAM chips, feeding the least significant 12 bits to the RAM chips and the most 4 bits to a multiplexer that goes to the 16 RAM chips. All of the RAM chips are on the bus but only the one with CE set responds.
The same kind of thinking could be applied to extend the address space past 16 bits, for instance you poke at some hardware register and that determines which chip enable pin get sets, there is really no limit on how much RAM you could attach to an 8-bit machine.
A really advanced bank switching scheme for an 8-bitter was on the TRS-80 Color Computer 3
https://www.chibiakumas.com/6809/coco3.php
where the 64k address space was divided into 8k blocks and which might be backed by 128kB (minimum), 512kB (max from radio shack) or more RAM and you poked into a table which mapped virtual blocks to physical blocks. That wasn't too different from a modern memory management system greatly scaled down with the exception that systems like that rarely if ever had a true "executive" mode so nothing stopped user mode software from poking to change the memory map. The CoCo for instance had a multitasking OS called OS-9 that did muiltitasking like described in the explained if you had the orginal Color Computer, you could get Level II that supported more memory and if you never poked at those registers, some memory protection.
[1] at least you did in 1979.