About all '51 clones can be configured to use external at least 64K (some more) of data/code memory (read about the EA pin...) but in most cases the memory won't be in-system programmable - you will need an external eprom/flash programmer, put the program on the expansion memory chip, then attach it to your device. The external memory replaces (overrides) the internal flash, so no way to use it like this.

Of course 4K of the internal flash is more than enough to write your own flash/eeprom programmer and use it to put programs in the external memory with slight hardware modifications comparing to standard external memory connection.