Legend of the Seven Stars

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Could you have a group of people writing together, each INDIVIDUALLY on the quest?

You could, though it should be noted that such a thread wouldn't be eligible for a Participation bonus. After all, the point of that bonus is to reward instances where members/characters are working with each other rather than merely writing alongside one another in the same place.

With only one person being able to carry the shard outta there, seems kinda wonky to increase the word count for dead weight, right?

It depends. While cooperation does increase the word count, it also makes it more likely you will secure the artefact in the face of any opposition. Plus, some people find it easier to write with others than they do writing by themselves.