You should just add the third partition like you did with the second os.
This guide should apply. Just replace Mint with Peppermint!
Just install normally. You can boot from your USB and follow the steps of the installer. You can either create a partition manually
before installing or use the tools provided by the Mint installer to
partition during the installation process.
The only thing you really have to worry about is when the installer
asks you whether to install a boot loader (GRUB). Then, you have 2
choices. Since you already have a GRUB installed by Ubuntu, you can
either choose to not install a new one from mint and use Ubuntu's or
you can install Mint's and overwrite Ubuntu's.
Use the existing GRUB.
When the installer asks you whether to install a boot loader, say no.
Once the installation has finished, reboot and load Ubuntu (Mint will
not appear in the list of available OSs). From Ubuntu, refresh GRUB so
it will detect your new Mint installation:
Use Mint's GRUB.
When the installer asks you whether to install a boot loader, say yes.
Make sure you install it in the same location where your Ubuntu's GRUB
was installed. This will probably be the master boot record (MBR) of
your primary hard drive. Reboot and you should now have Mint's GRUB
installed and will be able to choose Mint, Ubuntu or Windows.