You probably need Teensy 4.0.
TDM protocol is the only want to get 16 channels on a single data pin. Teensy 3.6 has 2 data input pins and 2 data output pins, so I just don't see any way for you to get 48 channels input to a Teensy 3.6.
Frank tested TDM on Teensy 4.0 during the beta test. But the code has changed a bit since then. If it's not currently working, report it here and I'll take a look. That should get you to 1 TDM input.
Whether 3 TDM inputs can really work on Teensy 4.0, I'm not 100% sure. My gut feeling is the odds are pretty good there should be some way to do it. But that way might require pretty difficult low-level programming. If you decide to try this project, please do so with the expectation that the published software really only supports 1 TDM data input and 1 output (16 channels in and 16 channels out).
Another technical issue is the lack of 16 channel codec chips. Pretty much all the TDM work we've done so far has been based around the CS42448 chip, using this circuit board:
https://oshpark.com/shared_projects/2Yj6rFaW
Here's the forum thread about TDM and the development of that board.
https://forum.pjrc.com/threads/4137...-on-Teensy-3-6?p=138705&viewfull=1#post138705
Perhaps with some digital logic to delay the FS pulse for 16 cycles, and to tri-state or mux or switch the 2 data lines every 16 cycles, maybe 2 of those CS42448 chips could talk on a single TDM channel with each chip's 16 most significant bits communicating during the 16 cycles where the other chip sends its low bits. So far, I'm not aware of anyone building such hardware. But it seems like this should be possible.
What definitely does work "out of the box" for Teensy 3.x is that CS42448 board with 6 inputs and 8 outputs.