I think the intent is probably as TarodNet says, though I have been playing in a group that has been running through these adventures one by one in sequence, and the DM pointed out this ambiguity at one point. They ultimately decided to give each person a magic item individually on the grounds of "go big or go home". Not saying that's right for everyone, but mostly you just want to think about how many magic items the party has already and what kind of tone the campaign has.
At the end of each chapter, the text reads "...the organization rewards the characters with an uncommon item of their choice as payment."
Is this one reward per character, or one shared by the whole party?
It looks like it's one item for the whole party: "... rewards the characters with an uncommon item ..."
THB a DM could gift more than one.
I think the intent is probably as TarodNet says, though I have been playing in a group that has been running through these adventures one by one in sequence, and the DM pointed out this ambiguity at one point. They ultimately decided to give each person a magic item individually on the grounds of "go big or go home". Not saying that's right for everyone, but mostly you just want to think about how many magic items the party has already and what kind of tone the campaign has.
pronouns: he/she/they
Maybe you can carnival prize it and give them the option of turning in three of the uncommon items for a rare.
"Sooner or later, your Players are going to smash your railroad into a sandbox."
-Vedexent
"real life is a super high CR."
-OboeLauren
"............anybody got any potatoes? We could drop a potato in each hole an' see which ones get viciously mauled by horrible monsters?"
-Ilyara Thundertale
Thanks for the input everyone, very helpful and appreciated.