RGB LED Strip controlling

I have to control 16 different rgb led strips, but i have only 11 PWM outputs on Arduino MEGA, and all analog pins are used as inputs. Is there a way to accomplish that? Maybe use one giant addresable RGB strip? Are shift registers compatible with PWM? Another ways of brightness control? What do you think?

Are shift registers compatible with PWM?

Yes when you use the ShiftPWM library
http://www.elcojacobs.com/shiftpwm/

Or maybe use three of these AdaFruit breakout boards. You will still need 3 MOSFETs per strip, if not using addressable strips.