The Coupé’s palette is 128 colours of which 16 can be chosen (MODE1,2&4) or 4 in MODE3 - see Screen Modes.
MODE1 has a ZX Spectrum compatible FLASH feature.
Originally the machine was envisaged to have 256 colours but limited to 64 colours due to a shortage of pins on the ASIC, see Hardware Bugs but had the extra intensity (BRIGHT) added on Simon Goodwin's suggestion in it's pre-ASIC design stage to give 128.
“I convinced them to do away with the hardware flash in the high colour modes. That allowed for a significantly larger pallet. I think it went from 64 to 128 colours. That also allowed me to transfer some pictures from the Atari without too big a degradation.”
The palette can be altered on a per-line basis using the line interrupts in MODEs 2-4 to give multiple colours on screen or to produce effects in the border area on the Splash Screen, see Fred 41 menu for a simple but effective example or demos by Matt Round and many others for complex ones.