Since FAT32 has already been covered, here is the only other alternative.
This will be hard. incredible hard.
Since for networking you have to not only implement hardware drivers, but the whole OSI stack, its not practical.
Add a COM port
If you get lucky it has COM support, but don't count on it.
Otherwise you have to implement a COM port in the kernel either by writing the code yourself or porting someone else's code over. Set the speed for 115200 or as fast as possible.
Then, another hard task implement X/Y/Zmodem.
However, compared to the effort of implementing as network stack this is easy.
This was the only option for old computers. The TI/994A has only this option.
On the PC side you can find old software to handle these file transfers already written.