You can use an EEPROM like a RAM, but only if you take its behavior into account.
You can simply connect:
- Z80-/MREQ to EEPROM-/CE, but you will need to gate this
- Z80-/WR to EEPROM-/WE
- Z80-/RD to EEPROM-/OE
Things to consider, consult the data sheet for details:
If you write a byte (or use the page write algorithm) the EEPROM will not output the stored values if you read it, until the self-timed write cycle has passed.
The write cycle is about some milliseconds long.
The EEPROM might fail after a few 10k write cycles (Thanks, Stefan Paul Noack).
You can't use it for the program that changes the chip's contents, because of point 1.
You can't use it for the stack or any other data that needs to be stored and retrieved quickly, because of point 2.
However, you can use it for the application's data. But you will need another memory for the program to run.
And if your program needs a stack or other variables to be written quickly, you will need an additional RAM. (Note: I remember a Z80 application that implemented a printer queue with just simple DRAM, using only the CPU's registers for the program's variables, and using the DRAM only for the data to buffer.)
To have multiple chip's as memory, you will need to gate the /CE-pins of these memories depending on their address range.