I've been doing the following to play both multiplayer & single player of different versions for several years: (works for both ETS2 and ATS)
Step 1: Make sure you have enough hard drive space (5-10GB) on a disk drive.
Step 2: Downgrade ATS / ETS2 to version 1.37 (the currently supported version in TMP).
Step 2A: To do this, open Steam, right click ATS / ETS2, go to "Properties", click on the "Betas" tab, select the 1.37 version. Steam will begin downloading & installing the files.
Step 3: Once ATS / ETS2 has been downgraded to the current supported TMP version, navigate to the Steam library folder (looks something like this: D:\SteamLibrary\steamapps\common and copy the ATS / ETS2 folder. Then paste it somewhere you can easily find (I placed my copy in the root folder (D:)
Step 4: Download the TMP mod and when it asks you where ATS / ETS2 is located point it to the folder you pasted in Step 3. NOT the Steam library folder.
Step 5: You can now upgrade your ATS / ETS2 Steam version back to the current version, in this case 1.38
Step 5A: To do this, open Steam, right click ATS / ETS2, go to "Properties", click on the "Betas" tab, select: "Opt out of all betas". Steam will begin downloading and installing files.
I recommend just starting a new profile for your TMP sessions, starting over fresh. Once TMP updates to 1.38, repeat this process from Step 3. In this way you can play multiplayer AND single player, at your choosing.