shift register RGB led brightness
Although you could run a shift register fast enough to PWM some LEDs, there are dedicated RGBA LED drivers which will take a serial input and perform PWM. One arbitrary example  is the TLC5971:


  The TLC5971 is a 12-channel, constant-current sink Spectrum PWM:
  driver. Each output channel has individually 16-bit (65536 steps) adjustable currents with 65536 PWM grayscale (GS)
  steps. 
  Also, each color group can be controlled by
  7-bit (128 steps) for each color group 128 constant-current sink steps with the global
  brightness control (BC) function. GS control and BC
  are accessible via a two-wire signal interface.