Shift address of eeprom?
Continuing from what Marcus already raised in the comments, you could likely use an ATTiny85 or even an ATMega328 to emulate multiple small to medium sized EEproms.
There is code readily available in Arduino land for reading and writing to program memory which in an ATMega328 would give you perhaps 28k * 8 without having to resort to external EEprom for your emulation device. The only point to be  aware of is that the program flash is only rated for 10k erase write cycles whereas an EEprom would be rated for 100k - 500k cycles. If you are just reading from your EEprom, this wouldn't be an issue of course.
You have plenty of pins to allow selecting pages of EEprom to serve up on the I2C bus and the code for an I2C slave for the AVR is again readily available .  

I'd suggest you could implement this on a small processor such as the Digispark Pro (ATTiny85 based) and get about 6k of storage, and 28k on the Arduino Nano and both could be powered by the EEprom socket. Both processors support USB so you could easily move EEprom pages to and from the device.