You can create root partition for Ubuntu MATE, /home for Ubuntu MATE, root for the 2nd distro and other partitions (like EFI partition, if you have EFI system and swap, if you want). As this 2nd installation won’t be used really often, it doesn’t need to have another /home.
You may also think about sharing /home between those 2 installations. I don’t really recommend it. Let me tell you a situation - Ubuntu MATE has Libre Office 5 and let’s say, that this another distro has Libre Office 6 and let’s say, that configuration files of Libre Office 5 aren’t compatible with Libre Office 6’s configuration files. A really bad problem may occur. Your choice. 