The installation of
grub has 2 parts: the resource files, and the boot loader. Each OS installation has its own resource files, but the boot loader is always installed on the master boot record. Effectively, the boot loader that is installed later will overwrite the former. In that sense, you can have only one full functional grub at a time.
I guess the tricky part (and your real question) is, how to make several Os'es work together in a multiboot fashion. This can be done in 2 ways:
The first is to make the main grub installation load the other OS'es. This is done my modifying the grub config (specifically the file
/boot/grub/grub.cfg) to include instructions on how to load additional OS'es. On some distributions (I think Ubuntu) this can be done automatically by an OS prober. This method is not very nice, as it requires changes to the main installation every time you upgrade the kernel, but it works.
The second is to make secondary OS'es install their boot loader on a partition rather than the MBR, and tell the main grub installation to chainload the secondary installations. I have a separate question on this (didn't really work for me so please add an answer if you make it). This method is elegant and is my preferred, however setting it up can be tricky depending on your luck.