sudo apt remove mate* (or sudo apt remove "anything*") is usually a bad idea.
You may end up removing things you really needed, and keeping things you
didn't want. Anything with "mate" in the name will be gone (such as anything
related to the "material" theme or icons), but a lot of the mate libraries
and utilities will still be on the computer.
I think the removal command for the mate desktop is sudo apt remove
mate-desktop. If you ask here how to delete a desktop or install something,
someone nice like chaosmonk or magicbanana or jxself will usually jump in and
help you fairly quickly. I try to help where I can, but I'm not as advanced
as those guys.
As to your earlier question, I forgot to mention that I added the Trinity
Desktop, so I could get the old-time 2003-era KDE 3.x experience again. I
really like it. So I guess I'm at 6 desktops now. I have a 750GB hard drive
with 544GB of free space, so it's not like I'm going to run out of space
anytime soon. In fact, there's really no reason to remove a DE unless you are
simply running out of space. I'm not sure why mate and Gnome wouldn't run
side-by-side for you, but they certainly should.
