As a DM, I would rule that each instance of Harm counts a single disease (probably)
When the Harm spell says that it's removed by effects that remove diseases, it probably means to say that it is a disease with respect to those effects. The first sentence of Harm's description supports this interpretation:
You unleash a virulent disease on a creature that you can see within range.
This means that if someone is afflicted by multiple instances of Harm, they would have to be either removed one at a time by an effect like as Lay on Hands or either version of Restoration, or all at once by an effect that removes all diseases like Heal.
But if you read the rules literally, maybe not
Harm's description says the following:
Any effect that removes a disease allows a creature’s hit point maximum to return to normal
Read strictly, this means that a target who is affected by 1x Filth Fever and 10x Harm, the Harms would all end if the target Lesser Restoration cast on them to remove the Filth Fever, since they the Lesser Restoration is an effect that removes a disease, and therefore triggers that clause of the spell's effect.
Similarly, if the Lesser Restoration removed the disease from the Harm spell, that one would be removed directly while the other nine would have their removal clause triggered (leaving only the Filth Fever in place)
I strongly doubt that this is the design intent, however, since it is a counterintuitive reading of the rules, which likely would have been expressed more clearly if it were actually what they meant.