For Teensy 3.x, to add one or several new USB type profiles, you basically follow the instructions found at the top of the usb_desc.h and then add a few lines in the \arduino\hardware\teensy\avr\boards.txt referencing the new profile(s) you have created (so they show up as selectable options in your IDE).
For example, in boards.txt in the Teensy 3.5 section, these are the lines for the default USB_MIDI profile:
Code:
teensy35.menu.usb.midi=MIDI
teensy35.menu.usb.midi.build.usbtype=USB_MIDI
teensy35.menu.usb.midi.fake_serial=teensy_gateway
So copy and paste that and change the values corresponding to your new profile in usb_desc.h. If you are using a Teensy 3.6, your lines go into the 3.6 section etc.
In your case, as you want to reuse an existing MIDI profile you simply copy and paste on existing definition in usb_desc.h and change the PRODUCT_ID, PRODUCT_NAME, PRODUCT_NAME_LEN values. Choose a PRODUCT_ID that is not yet used by any of the other profiles defined in usb_desc.h. You also need to use a unique #if defined(YOUR_UNIQUE_PROFILE_ID) line for each profile.
If you want multiple USB profiles, simply copy and past multiple times, choose unique PRODUCT_ID, PRODUCT_NAME, PRODUCT_NAME_LEN values and add the lines to boards.txt for each.