TinyMCE profiles: can user choose from multiple profiles available to his role?

With the latest TinyMCE, I finally have pre-5.x TinyMCE functionality restored to my 5.x sites. Where can I send new Porsches to the people responsible? : >

But first, simple questions:

TinyMCE allows setting up profiles. This is great so that top admins can have an advanced profile chock full of buttons, and anon users can have a simple profile with just buttons for the basics (bold, italic, etc.).

But say I make both the above profiles available to a role, such as authenticated user. How can an authenticated user choose which one he wants to use? Currently, TinyMCE delivers one of the two profiles, and I see no way for the user to select the other profile, whether there among the TinyMCE controls, or in the user's own profile. (The only TinyMCE-related bit I see in the user profile is the ability to select whether the text editing controls are turned on or off by default for that user.)

The workable, if unsatisfactory, solution might be "don't give a role access to multiple TinyMCE profiles". But where I'm facing the problem is for me, ID 1. The ID 1 should automatically have access to any TinyMCE profile. I have two TinyMCE profiles set up, yet Drupal makes the choice for me. At first it was giving me only the simple profile, when I want the advanced. Then it started giving me the advanced, which was good. Now it gives me the simple again, for reasons I don't know.

Is there some way a user with access to multiple TinyMCE profiles (including user ID 1) can choose the preferred profile?