Hi folks.

Though I am stuck in the problem of not being able to program any more Arduinos, I was wondering about the existing one which IS working.

My sketch has grown and I realized that I am out of memory.

Is there any way to increase the size of the usable memory on a UNO copy?

PROGMEM - Arduino Reference to move large strings into flash. Beyond that you need to move to a Mega, and beyond a Mega's memory size you can add external memory.

Or post your code (if you can) and see if it can be memory-optimized somehow.

Bummer that Quadram doesn't work with Uno...

Which memory have you run out of, flash or RAM? It is often possible to change the code to reduce usage of one or other or both, but you need to post your code if you want specific advice. Once you have applied the main techniques, if you are still running out then the best option may be to switch to a processor with more resources, e.g. a Mega or a Teensy.

You can move to a board with a '1284P chip if you need more SRAM - 16K, twice what a Mega has.
I offer a 1284P that you assemble. 128K flash, 16K sram, dual serial ports, 32 IO pins.
Cross Roads Electronics for PL and schematic
$5 mailed to US locations. Order parts you need, or scrounge your parts bin.

These can be mounted on a shield, DIP8, and they work at both 5V and 3.3V too.