Potion of Halitosis question

[Eniripsa]

I read quite few situations about the floating nose and potion of halitosis, but didn't find the answer to this:

A player is fighting the floating nose and is winning by a small margin. Another player uses the potion of halitosis to increase the power of the floating nose to make the first player lose.

Is this allowed or does the potion have to kill the floating nose when used on it?