I don't think that a question should be closed or opened by three "random" votes. On the other hand, we could "get there" in a roundabout way by giving certain individuals "double" votes.
This would be a user privilege, whereby users with 10,000 rep (or some other threshold) could effectively cast TWO close or reopen votes instead of one. THREE such users would cast six votes. Or it could be two double voters and one single voter, or one double voter and three single voters or the current five single voters to add up to a total of five.
That way, we would retain the "fabric" of five close or re open votes, while allowing close or reopening by three "senior" users instead of five users or one moderator.
Another possibility is to allow moderators to choose to cast a "double" vote instead of "five" votes. Many moderators shy away from unilaterally taking "five" vote actions in order to defer to the community, but would welcome the chance to "personally" cast single votes, and probably would welcome a chance to cast a double (multiple) vote that recognizes their seniority. Of course, they would retain the right to cast "unilateral" votes in the case of spam or bad (not just mediocre) content.
Edit: New sites in their "start up" period would have reduced thresholds for "double votes" on closing and reopening, just as "single" votes now do.