Are you wanting to turn on/off each of the 16 lamps in each of the segments individually, or just turn on/off all 16 lamps at the same time. If they are RGB, do you want to be able to change each of the RGB components of each lamp?

If I was going to do this I would either look at DMX and addressable LEDs / drivers, or, if you still wanted to do this with a PIC, then I would use 3 x PCA9685's per segment, one each for the individual R, G and B segment for each lamp. This way you can not only produce whatever colour you want, but also any brightness you want, and if you're clever even have it chasing and making patterns.