I would double check if you are talking about a purchased ArcMap/Decktop license at the same time as EDN. Typically EDN is all the server side software, and Desktop is purchased separately (or as an "add on"). So, you can install different versions of EDN "server" (e.g. ArcGIS Server) on separate servers for testing/developing, however, the Desktop might still be limited to one install/registration. Base on the "what-you-get" page, if you are purchasing it as the "add on" with you EDN, it looks like it is just a single-use....and at whichever level you pay for (basic or standard or advanced). But to be sure, always best to talk to customer support or your local distributor.
If the Desktop license is a concurrent license that you purchase separately ( and not single-use), then you can install Desktop on multiple machines, but can only access it on one machine at a time.
But as Dan mentioned, you don't want to mix 10.0 and 10.4 on one machine of any of the software.
btw - another option if not being used for work or profit, etc. ArcGIS for Personal Use Program | ArcGIS for Desktop Advanced for Personal Use Cheap...still locked to one machine...but good if you want to expand your knowledge at home, etc.