200+ inputs and outputs: shift registers, multiplexers or other options?

Thank you for the usefull suggestions! So for the leds I'm definitely going to use the max7219 chips and multiplexers for the pots. Using a matrix for the buttons looks like a good solution, but there is one problem: the arduino I wanted to use doesn't have 28 input pins. I wanted to use a arduino with an atmega 32u4 chip, since this chip supports midi over USB. Can I use multiplexers for the 28 inputs or is it better to use an arduino mega and built a midi output circuit? Or are there any chips like the max7219 for inputs?