From TactWiki

These are quests in the Web Series in Qalia.

Go here for information on the Thestran Web Quests

The threads start in four different locations, and merge at the third and forth quests. At the end of each thread, you will be directed to the other three quest starters. The quest A Finer Suit is only offered once you have completed all four threads and combines the four suits into one.

These quests are meant to be done one line at a time. Taking multiple quests in order to be "efficient" will only result in having to petition a GM to reset your quest counter.

Rewards and Final Combined Suit

When you complete each quest, you will receive an item that has either Crafter, Clergy, Noble or Outsider presence on it. For each quest line, you should select the same type of presence for your reward, i.e. for the Khal line always take Noble then for the Lomshir line always take Crafter etc. This way, when you have completed all four lines, you will end up with four complete suits. At the completion of A Finer Suit, you can turn all four sets in for a set that combines all 4 presence rewards on a single item.

It is possible to take the same reward twice, so that you double up on one item and are missing another. If you do this, you can trade in the duplicate for the one you need when you visit Weaver Jekaqie to turn in A Finer Suit. See the quest page for descriptions of reward items.