Unfortunately you cannot. Some people have claimed that you can try to de-solder the memory packages and then solder on bigger ones but I have a feeling the success rate on such an operation is fairly small. The ICs have to share the same exact pin out, power requirements and architecture for this to work (on top of the soldering being successful). The iPhone also contains no external memory components so you can't use anything like an SD card to expand the memory.
The only other option I can think of would be to do a logic board swap to a larger memory size...but for the price you are close to a used phone.
Hope this helps, good luck!