The only quest that counts for this is from Spencer Rye in Abah's Landing.
That quest is once per day.
So a player with one character could not complete this in one week. Last week, this quest could be claimed THREE times, that is 24 repeat quests. This week, I have it as SIX times!
IMHO, a WEEKLY quest should be able to be completed by one character in 7 Days. Not via multiple characters, not by asking for quest shares, not by rolling over to the second.
I know I can just reroll it, but I save those for when I have a challenge that is something I don't want to do, rather than something I can't physically do.