Microchip.com has a 512K-bit serial EEPROM that they manufacture,
but it stores just 512 * 1024 / 8 = 65536 = 64K bytes.
This is a lot of storage, but I am wondering if there any companies
that manufacture even larger I2C serial EEPROMs? (preferably coming
in an 8 pin DIP package).
I've been looking for the same but haven't been able to find any. It seems that as the data capacity gets larger, higher speed is demanded. For this reason SPI is preferred. I'd recommend switching or just using multiple of the 512k chips. You can put up to 16 on a single bus.