How to read/write beyond the first 256 bytes of EEPROM

I am using an Ixora 1.3 board with Apalis iMX8 SOM.
According to an answer in this post, we “can use the EEPROM (AT34C02D-XHM-B 2-Kbit (256 x 8)) for your own needs. However we do not recommend to use the lower half (first 128 byte) if this EEPROM”
I am able to skip the reserved block and read/write the second 128 bytes no problem using

echo -n -e "{str}" | dd of=/sys/class/i2c-dev/i2c-4/device/4-0050/eeprom bs=1 seek=128 conv=notrunc

to write and

dd if=/sys/class/i2c-dev/i2c-4/device/4-0050/eeprom bs=1 skip=128 count=128 2>/dev/null

to read. However, I am not sure how to access the eeprom beyond the first 256 bytes.
TIA

The EEPROM is only 256 bytes in size, there is no additional storage.

Many manufacturers specify their EEPROM sizes in kilo (or mega) -bits, you need to divide this number (2kbit, or 2048 bit, in this case) by 8 to get kilobytes (256).

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If the EEPROM is limited to 256 bytes or 2-Kbit (256 x 8), it’s impossible to access any data beyond the first 256 bytes. Should you require additional storage, you have the option to install a larger EEPROM on your carrier board.