I'm not quite sure if you know that there can only be 1 operating system on a machine at at time (except for virtualization, but that's not important). The image of the operating system can be written to the hard disk so that it's loaded onto the CPU at boot, but that doesn't mean that multiple OS's can occupy the same CPU simultaneously. That would cause chaos.
That being said, it is possible for one to install three different OS's onto the disk, but you'll basically have to boot up each one separately each time.
If you're looking to test-drive Mint, you can go to the download page, get the '.iso' file, and burn it to a flash drive to test it out. If your computer doesn't automatically boot from the flash drive at startup, you may need to change the boot order in your computer's BIOS temporarily.
The reason that I suggest this method is that Linux Mint provides a test-drive version of itself with no permanent change to the disk; everything is lost from RAM when you shut the computer down again. Ubuntu provides a disk image, too, but I'm not sure if you will be able to burn this image to a flash drive as with Linux Mint, since I know that Mint uses a special cross-medium image.
If you're thinking of dual- or triple-booting your computer, just forget it ever existed now. This breaks stuff. If you must, put the Linux distro in a virtual machine or on another computer, since Windows and Linux are at each other's throats even being on the same hard drive.