There are 2 ways to think about I2S (or any other hardware) capability.
1: Hardware specs - what is possible if you write your own drivers and all the code
2: Well supported software - what you can do easily, with little or no modification to existing libraries (device driver level code)
For example "Is it possible to work at 24bit?". Yes, 24 bits is certainly possible. But the Teensy Audio Library only supports 16 bit sample size, so to work with more bits you'd have a write quite a lot of code!
I2S is fundamentally a stereo digital audio communication protocol. One I2S data stream always carries exactly 2 channels.
The Teensy 3.2, 3.5 & 3.6 hardware has dual I2S input and output. So using I2S, you can have at most 4 channel input and 4 channels output.
The SAI hardware can support other non-I2S protocols. TDM is supported by the audio library. Currently
the only well tested TDM chip is CS42448, which provides 6 inputs and 8 outputs.
Something to keep in mind is the SAI (Synchronous Audio Interface) hardware generally only supports 1 protocol at a time. So if you use it for TDM, you can't also use it for I2S. So you can't do something like connect a CS42448 chip and then also connect the SGTL5000 chip, as on the
audio shield.
Likewise, the SPDIF output and PT8211 use the SAI hardware in other modes, so you can't use I2S or TDM while using either of those.
But you can use the on-chip DACs and ADC (singular) for 2 more outputs and 1 more input, at only 12 bit resolution. This is well supported by the audio library, so using those while also using I2S or TDM or SPDIF or PT8211 (mutually exclusive "or") is as easy as just dragging their symbols onto the design tool canvas and connecting them into the system you intend to implement.
If you're not familiar with the design tool and audio library, I highly recommend starting with the tutorial.
https://www.pjrc.com/store/audio_tutorial_kit.html
There's a 31 page PDF manual with step-by-step instructions and a full 45 minute walkthrough video which comes in handy if you get stuck & need to see how a step is done.
Of course, this already-written library and the tutorial material is the answer to question #2 - what you can do quickly & easily by leveraging existing libraries.
If you instead intend to write all your own code, then the answers you seek can be found in the reference manual for the chip.
https://www.pjrc.com/teensy/datasheets.html
For example, if you read the MK20DX256 manual, the SAI chapter begins on page 1297. If you believe you'll take path #1, I would highly recommend trying to read that chapter, and also the chapters about DMA. Maybe also look through the
audio library code on github. This library is the result of about 4 years of work. Earlier efforts in 2012 & 2013 are still around in very old threads on this forum, if you want an idea of what starting from scratch looks like! I can't emphasize enough how many hours of pretty advanced level coding are required to develop high quality & easily usable audio processing code. If you really do intend to go that route, of course I don't want to discourage you. But do so with a fully informed idea of the work required.
But for 16 bits and a pretty large feature set, as you can see in the tutorial, the existing library and design tool makes it very easy.