I want to enable at least some users to modify reviews after they are completed

Interesting.  Similar to the inspection/annotation phases that happen before the actual review, you could also add a "Post Review" phase with corresponding fields that are required to be filled out by specific roles after the real "review" work has completed (inspection / rework phases) - if that were the case, Collaborator could also enforce this 'analysis' portion of the review cycle / send reminders / etc.  Obviously if the customer didn't want to add any post-review analysis to the process, we would want the record to jump straight to the Completed phase as it currently works.  The reminder the currently author gets to commit artifacts to source control for pre-commit reviews could also possibly be included in this "Post Review" phase.

I like where you're going with that, Dubya....

I don't really want to add a new state.  Not all reviews will need changes or quality reviews, so some will sit in that state forever.  That's a pain in the neck.  

Maybe the state could be optional - for example if no post-review analysis is required, the creator could "Dismiss" the action similar to the reminder to commit changes for pre-commit reviews.  Some groups (such as mine) probably would want to enforce the process for every review so keeping it in the state until the work is done would be a good thing from my perspective.

The creator will not be the decider if there is a "post review phase", and the person(s) who would do this post review would complain about having to move all the reviews that they don't want to qual check.  I'm not opposed to a Post Review State, but it doesn't solve my problem.  I just want to allow at least some users to be able to edit the general review fields after it is closed.  This could also be useful for "fixing" the data fields after the review is closed.

Would be nice if it allowed the flexibility to support both use cases; one of the strengths of Collaborator is it helps enforce that users follow their organization's review process, and I think that should cover the entire review lifecycle, including post-review work.  I'd prefer the option to configure the extra "post review" state (rather than just include it in "Completed") because often there is pressure to show that the review has actually been completed & findings closed, and you wouldn't want "non-critical" post-review work to slow that down.