I had XFCE once and did not liked it at all.
I like Mate very much Clem, Stefano and team did excellent tool out of it.
Although for Clem it is like secondary project as I guess his beloved kid is Cinnamon
If you are not happy with XFCE just drop it and go for Mate.
You can have two UI installed, I had it like that years ago.
If you don’t play to much with libs and don’t create too much confusion with your graphics shells it is likely to last.
Although if you decided on environment there is no point to keep second one.
Linux is collection of software, there is no point in mixing sets.
I think command for installing full mate desktop will be.
sudo apt-get install mate-desktop
But google it and maybe ask around, if you are not prepared for troubles and full reinstall.