I did it in Debian 7 with no real dramas that I can recall and I'm currently running MX-16 XFCE with MATE 1.16 on a test machine. MATE 1.16 from stevepussers Opensuse repo. Again, no significant issues but you will need to deal with some duplications in the menu system as one desktop or the other drags in apps for the other. I did have a minor problem with moving windows causing a system freeze and losing window borders. That was tracked to compositor settings which were then easily fixed. Atril needed the 1.16 version.
Similarly to running MATE with Gnome installed on the same machine you may find some desktop related apps that will run in one desktop but not the other. Users and Groups was one example of this.
So, generally speaking, not a big problem having two desktops installed but will need a little tweaking. Unless really necessary for some reason I think I'd prefer to install with a single desktop and have dual booting to another instance with the other desktop. Cleaner and more likely to avoid GTK conflicts where one runs a different version to the other.