I’m not familiar with The Sword, but are the characters in the party competing against each other? If so, how do you see that working? Not sure if that is what you meant.
On the other hand, having a common goal is a great way to start a campaign. If they were all trying to get the item together that would encourage teamwork and camaraderie. Maybe they are competing against another adventuring party or even against different benefactors to get the item before the other rival.