I suspect the debuff won't stack, but that's not saying it won't.
I would suspect also, that once consumed it can be reapplied.

In either case, its a substantial strain on healing.
Either they stack and are all cast at once, or you apply them in rapid succession to the target you are burning, with each attack reducing the effectiveness of the heals.

In a way, boxing takes a mechanic which is interesting or neat for 1 toon of the class, even in a party... but multiplies the effect in fun ways.
Four totems is not unbalanced really, but twenty totems each basically affecting the whole party...
Never know, the heal debuff might well stack initially, and if it does there's a good chance it will stay.