Old TPMS vs. Newer TPMS

The TPMS on my 2013 Tundra works fine on the original aluminum wheels. I just got a set of steel wheels from a 2017 Tundra and they have the TPMS still in them. I want to put real winter tires on the steel wheels and then just swap wheels/tires to the more highway friendly tires on aluminum wheels for long trips and summer. (live in the North). I asked my dealer and got a confusing answer about older Tundras couldn't deal with two sets of TPMS codes. I looked a bit on line and it appears that some TPMS units can be re-programmed (obviously the ones from the parts store must have that capability?). So can I use the 2017 TPMS on my 2013 truck, do they or the truck need to be re-programmed, do I need re-programming every time I swap them?

 

Every time you swap out the assemblies, you will have to re-program. I think the ECU can only store up to 5 TPMS IDs at a time.

 

From some of the YouTube videos I get the idea that the individual TPMS units can be re-programmed to mimic the original ones, if that's true what would require reprogramming with each swap?