Would there be a problem with running Web Adaptors of different versions, e.g., 10.3.1 and 10.4, on the same machine? I will have servers (production and testing) running ArcGIS Server at different versions so I want the Web Adaptors running on the web server (no AGS installed) to be at the same version for the server they will connect to.
You can install ver. 10.3.1 and 10.4 of Web Adaptor in a single web server. You just need to take care that during configuration, the Web Adaptor's version must always match the version of its registered ArcGIS Server site. Also provide different names for each instance of web-adaptor.