You can MQ on the same account, I've done it 100's of times. The initial item(s) stays available to the next person until someone either finishes the quest again or the server resets.
I'll often hand in part and then camp or Q over to a diff char to finish it.
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-Happyfeets/Crappyfeet/Crackyfeet/Abraham, TMO
The Plague of Fennin Ro
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