You can do that part of the quest with anyone as long as you run it with one of each class. The other two don't even need to have the quest.
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Really? Do you need other people with the quest for other parts, or can you be the only one with it as long as you have 1 of each?
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Yep, the only part you need someone with the quest is the code parts. That part isn't super picky either, if you know anyone that has finished the quest, they can get another siva engine from Shiro to do it with you.