Well, you are going to need logical volumes. So something like
Code:
/dev/sda1 - boot
/dev/sda5 - swap
/dev/sda6 - Fedora
/dev/sda7 - Mint
/dev/sda8 - Ubuntu
Now, the tricky part will be to install 2 out of the 3 of those without installing grub. So you *do not* want grub installed from Fedora nor Mint. But their installers might not give you the option =(. What you might do is install them in the order Fedora, Mint, Ubuntu, pointing to sda1 as /boot each time, and backing it up before the next install. You'll need all of the kernel* vmlinuz* System.map* etc, for each distro. Finally, install Ubuntu last and copy all of the boot files over to the same boot partition, and uninstall grub from Fedora and Mint. If you can get it, this is the cleanest option IMO.
Another option, which would be much easier to setup AND maintain, would be to have a separate boot partition for each OS, and use Grub's chainloader feature to point to the others. In this case, you might only want:
Code:
/dev/sda1 - Ubuntu
/dev/sda2 - Mint
/dev/sda3 - Fedora
/dev/sda4 - swap
set the BOOT flag on sda1. When you are installing each OS, don't create a separate boot partition. This option also gives you the flexibility to copy over the boot files from each OS to any of the other's boot directory, so you can skip the chainloading if you want.