The answer to your question is "yes and no" as it is phrased. Effectively, though, it is "Yes."
At the level of each user account you can choose your default apps for most commonly performed tasks (e.g., web browsing, playing media, etc.) and can even drill down and assign default apps by file type on an individual user basis.
Most of the time when you install things like MS-Office and Libre Office they will ask if you want to associate the file type or types they normally handle with them and most commonly that occurs across users (though sometimes not). In the case of office suites the default extensions are different and there's not much if any overlap with what they will open by default. You can, of course, set Libre Office Writer as the default program for docx extension files, but what its own default happens to be is for odt extension files. Of course, Microsoft Word can also open odt files, too.
In the end you can achieve precisely what you're seeking to do, but it may involve going back to the respective accounts and tweaking the default programs based on what you installed, in what order, and whether the install could be limited to the current user or is applied to all users.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
In a modern society where everyone thinks their opinion deserves to be heard nothing annoys me more than individuals who mistake their personal preferences for fact.
~ Commenter TheCruyffGurn on the The Guardian website, 8/13/2014