If you just need more RAM for a display buffer there are much faster devices than an external EEPROM, like the 23LC512 serial SPI SRAM.
Also, since SHIFTOUT runs at approx 50KHz, you could even write your own dedicated version that would be MUCH faster than that, although using the MSSP/SPI peripheral is pretty straight forward and would easily get you into the multi-MHz range.
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