Yes, using multiple boards is certainly possible.
Without knowing anything about your project, I can only give very generic advice...
Using them as mouse, keyboard and joystick, the main challenge is the PC side software which is mostly designed to use only 1 of each device. When you plug 2 normal USB keyboards into the same PC, the drivers on the PC side merge their data together so typing on either controls your PC the same way. You can expect the same using Teensy - since it's just another keyboard as far as your PC is concerned. Again, not knowing anything about your project, it's hard to know if this is what you might want, or if you need each to control some separate program.
Likewise with the other USB types, the main issue is how your PC handles more than 1. With USB MIDI, there's an example showing how to change the name which appears.
The other less-than-ideal aspect of using more than 1 is the Arduino IDE. It's designed to be simple for 1 board. You can use more than 1, but it's a bit cumbersome. At the very least, you need to use Tools > Ports and Tools > Boards (if not the same model) to switch back and forth. In some cases where a specific Teensy port isn't selected, it will automatically try to upload to the first board it can find, which might not be the one you want. All this stuff is only a minor inconvenience, but something to mentally prepare.