RE: TPU on MMU3
Here is a simple procedure:
In PrusaSlicer, go to the Plater tab and select the Original Prusa MK4S 0.4 nozzle printer (or another TPU-compatible Prusa printer). Go to the Filament settings and choose your desired TPU profile (e.g., Prusament TPU 95A @MK4S). Click on the Dependencies tab. In the "Compatible printers condition" field, delete the text: and ! single_extruder_multi_material Save a copy of this new profile.
The profile will now be compatible with printers equipped with an MMU.
RE: TPU on MMU3
I played around quite a bit with different settings and hardware modifications to get TPU to work on the MMU3, not only during single-material prints, but with true multi-material prints (so for example TPU and PLA). I have finally got it reliable enough to attempt big prints (so 100+ filament switcher in one print). I made a guide on Printables with all my components and settings, in case someone else wants to attempt this too:
https://www.printables.com/model/1356306-mmu3-printing-with-tpu-parts-and-settings
Here is a sample print that I did:
