Is it possible to change skins in TinyMCE?

I’ve posted this already in the “How-To and Troubleshooting” forum, but the problem appears also if you use TinyMCE Advanced and Advanced TinyMCE Configuration, so I thought I’d repeat the post here.

In a multisite, I’ve been trying to change the skin in TinyMCE from the default to some of the other skins from http://www.tinymce.com. I set the skin setting in Advanced TinyMCE Configuration. However, it does not work. An inspection of the editor in Firefox shows that the different skin (skin.min.css) gets loaded but is matched and superseded by editor.min.css of WP, which always produces the “lightgray” skin in the editor (and which, by the way, differs from the “lightgray” skin in TinyMCE itself).

If I disable editor.min.css in the inspector, the different skin shows up, but the Visual-Text tabs and the Add Media button get messed up (they move above the post title field and the tabs turn to simple links).

Is this intentional? Will setting a different skin lead to some sort of trouble and that’s why it has been effectively blocked?

If not, is there a way to let the different skin show without loosing the functionality provided by editor.min.css?

https://wordpress.org/plugins/advanced-tinymce-configuration/