I just got a new pc and installed windows 10 and I am a big linux fan so of course I setup dual boot with ubuntu 15.10 but I would also like to setup linux mint. I have checked out other questions like this but they all start without ubuntu installed. Is it still possible for me to add another distro after I have installed ubuntu?
3 Answers
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.
A) 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:
sudo update-grub
B) 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.

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make partition for new distro and install, should be fine. after install update grub
you can update grub without rebooting to ubuntu by using chroot, like here
also you probably could edit /etc/fstab to have same /home mount point in every linux installation, but i wouldn't do that, something could go very wrong :)
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Assuming both are either UEFI or both BIOS, just be sure to install in same boot mode. I have multiple Ubuntu installs and use about 25GB for / (root) but have large data partitions. When I still had XP years ago, I used NTFS as a data partition. Windows 8 or later makes it a bit more difficult as you must have fast startup off or even a data partition is still mounted with the hibernation(fast start). – oldfred Apr 04 '16 at 21:20
Install Ubuntu first with a partition (Remember your UEFI permissions) then after that instalation Mint will ask you if you would like to install alongside windows and mint, if not use the "something else" partition