Kenneth Konyndyk's Introductory Modal Logic claims (p. 55) that all formulas in S5 with a modal degree greater than 1 can be reduced to degree 1. By degree, he means the maximum number of modal operators that any one sentence letter is in the scope of (e.g., ◊p has degree 1, □◊p has degree 2, (□◊p v ◊p) has degree 2, ◊(□◊p v ◊p) has degree 3).
Konyndyk doesn't really explain how to do this reduction. He gives exercises where he asks the reader to reduce several formulas to degree 1, but he never goes through an example that uses a two-place truth function, so I have no clue how to do it.
For a specific example, how would you turn ◊(◊p ⊃ ◊p) into something where each instance of p is only in the scope of one modal operator?
For another example, how would you turn □(p v □q) into something where each sentence letter is only in the scope of one modal operator?
Edit: By "reduce," Konyndyk means that there should be a necessary equivalence between the iterated modality and the single-degree formula, so it's not enough to derive a simpler formula if that formula can't also be used to derive the starting point.
Edit 2: I can only use Fitch's natural deduction laws to transform formulas.