The way it's currently written:
Range("Claimed", "Closed")
doesn't represent 2 distinct areas but one rectangular block. For example, if Claimed was just a single cell D3 and Closed was a single cell K33, Range("Claimed", "Closed") would be D3:K33. It makes no sense to add another range to this.

However, if it were written:
Range("Claimed, Closed")
(note how the quote marks have gone in the middle) this does refer to 2 distinct areas. Now it does make sense to add a third area:
Range("Claimed, Closed, AnotherOne")
but be aware that the code will only write something to the sheet if you double-click in one of these areas and won't if you double-click between them.

ps.
Cancel=True
somewhere in the code, preferably within the If statement if you want users to be able to edit the cell if they double click outside the designated area(s), will stop the cell remaining in Edit mode, so you won't need the ActiveCell.Offset(0, 1).Activate.