As of a few minutes ago, if you have a gold tag-badge for a tag associated with a question that's been closed as a duplicate, you can edit the duplicate links to replace, add, remove or re-arrange them:
These changes are tracked in PostHistory to allow anyone to detect abuse, while the results update the PostLinks table so that existing logic continues to work (I mention this because some of you may wish to lean on SEDE for observing how this works out, once it gets updated).
This has been requested for... Oh, about four years now. In February of 2013, Jarrod replaced the venerable but messy method of marking duplicates by editing links into the top of the post with a system that records the question IDs in a separate table and renders them as needed. This was a huge improvement... Not only did it make tracking the usage of duplicates much easier and more reliable, it also prevented editors from inadvertently (or intentionally...) editing out the duplicate links without reopening the question.
But it also prevented anyone from updating duplicate links, which was useful in cases where more than one duplicate was appropriate (for instance, "too broad" questions that consist of multiple questions, each already answered) or situations where the asker clarified their problem and a different duplicate link became appropriate.
This was clearly not ideal; some folks resorted to reopening and re-closing, while others savagely abused bugs to work around the deficiency.
Today, that changes. Oded stepped up to implement an elegant solution: allow users trusted to single-handedly close questions as duplicates to also modify the list at will.
This stops short of fully restoring the previous capabilities - after all, there were serious downsides to that. But it should suffice to allow those most familiar with a given topic to better curate it.
Please report any bugs you find, tagging them exact-duplicates dupehammer. Enjoy!