On a Dual boot (Grub default) Win10- Ubuntu18.4 system on a Dell Inspiron 15 3567
I want to install Peppermint9 as a 3rd system- will it figure out how to add itself to the Ubuntu GRUB, overwrite GRUB with it's own and all 3 systems, destroy it so nothing boots, or how do I do that myself?
You should just add the third partition like you did with the second os. This guide should apply. Just replace Mint with Peppermint!
https://unix.stackexchange.com/a/155406
Ubuntu found the aborted Pep installation (bad disk) on an update and added it, but Peppermint overwrote it with it's own more primitive bootloader, which found all OS's.