In more complex projects where audio or video are involved, microcontrollers usually run out of internal RAM. The only solution that stands out is adding external RAM. Depending on platform and solution used there are many ways of doing this. But usually goes SRAM modules, latch register(s) and probably some other additional circuits. If you only need to add more RAM without planning all this you can use RAM module like this one made by [Wardy].
This is simple RAM module with 512Kbytes of static RAM. It only needs 13 pins for interfacing and can accept voltage levels 3.3V or 5V. PCB layout is designed so that pins are breadboard compatible – easy to play with any microcontroller or dev board like Arduino.