Every time you tame the new mount there is very small delay when you can see achievement for taming and still alive creature. You can see this situation on the screenshot:
In this moment you have Midnight Panther tamed, and another person can use his Music Box, he will tame it as well.
So it is possible to tame it with few players, but all of them must use Music Box (to have 100% sure of success) in ~0,5 second after first player has tamed the mount.
Another option is to tame and kill panther at once. Just use Music Box on Midnight Panther when it is on it's red HP and hit strongly, for example with Sudden Death Rune.