It isn't really possible with an Uno, since I don't believe it has any way of extending program memory. If you have filled up your program memory with strings and read-only data using PROGMEM, you could move these to using a micro-SD card, and read in the values when you need them, or use a i2c/spi memory expansion chip instead of the micro-Sd card. You would have to restructure the program, and move even more out to external memory, as the libraries to access these devices will take space.
A much simpler solution is to use a Mega 2560, which has 256K of program memory, instead of 32K (and 8K of SRAM memory instead of 2K).
Or if you can run your devices at 3.3v instead of 5v, the Teensy 3.1 (which uses an Arm processor instead of the AVR processors used in the Uno/Mega) also has 256K of program memory (and 64K of SRAM memory). Similarly, the Arduino Due has 512K of program memory and 96K of SRAM.