Is it possible to toggle among different OS in a multi-boot PC without restart

I asked the IT guys to try removing the PCI/PCIE cards that were installed to see if they were affecting the shutdown process.

Sure enough, removing a Moschip Semiconductor serial/parallel port PCIE device resolved the problem.

If you want to hibernate and use a different OS while Windows is hibernated you must not put the Windows bootloader first, contrary to what @snayob says.

If the Windows bootloader is first, the very first thing it does before showing the menu is check for a hibernated OS. If a hibernated OS is found, it will boot into it automatically and will not show you a menu to choose boot options from. If you force the menu (i.e. F8), the hibernation data will be deleted.

Now if GRUB is the MBR boot menu and is configured to chainload BOOTMGR or boot into Linux, you can hibernate Windows and boot into Linux - but if you mount the NTFS partition, most likely your hibernation will be lost (detected as corrupted). Basically, if you hibernate a machine, you must not touch any volumes that were mounted on that machine (i.e. any FAT32 or NTFS partitions assigned a drive letter in the hibernated OS).

Ridiculously important note: In the event that you mount (say, in Linux) a Windows partition while Windows is hibernated and you are unlucky enough that when you're done with Linux and attempt to reboot into Windows, Windows does resume from hibernation (instead of erroring out, throwing away hibernation data and attempting a normal boot), you will most likely suffer catastrophic data loss to all Windows partitions as all filesystem-related structures will be out-of-sync between what Windows has loaded in the memory and what's actually written on the disk.

Other than that, there's no problem. Just install Windows, Ubuntu, and Fedora. Make sure the latter do not automatically mount Windows' drives on startup, ensure GRUB is the main bootloader, and you should be able to do what you want.