BelligerentPacifist
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A different diameter requires redesign, and a small change requires enough reengineering to make your missile a new missile.Wider body will face higher resistance and drag besides that would require all the internals to be redesigned as well, which in my opinion is not an efficient way to add range To increase range of an existing missile the easiest and most efficient way is to either increase the length or add another stage, which separates from the main body after fuel consumption thus reducing weight and drag.
Serial staging would only work if the lower stages have enough juice to carry several more tonnes on their heads. It often does, but then you ask yourself the question whether you've added to the range.