Hello, frsu.
Very likely we have read similar threads about installing the Mate desktop and the Cinnamon desktop side by side. and we both have not bothered to bookmark any of those threads for future use.

Mate brings along a fork of the former Gnome2 desktop software, all renamed to mate-something.
Cinnamon brings along a fork of the current Gnome3 desktop software and quite a few genuine Gnome3 software packages.
So they can live side by side.
I assume that a potential problem will be double menu items for all those programmes which come in two diffrent flavours: a Mate flavour and a Cinnamon flavour. - Yet, I have not tried, so this is an assumption only.
Installing Cinnamon in addition to Mate should be fairly easy:
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sudo apt-get update
sudo apt-get install mint-meta-cinnamon
The mint-meta-cinnamon package should make sure that all software packages which are required for the cinnamon desktop and which are not present on your system will be downloaded and installed.
As said before I assume there may be an issue with double application menus and items.
There also may be an issue with the default file manager which handles the desktop: caja (Mate) vs. nemo (Cinnamon).
Yet, all such little nuisances should be solvable.
Cheers,
Karl