Merging columns but ignore repeating items across a row

It sounds like you want the set of all possible subsets of these four symbols.

If that's correct, you may be interested in my comment on smpa01's combinatorics blog post. In particular, you can generate the list of combinations as follows:

let
  Source = {"(*)", "(^)", "(!)", "(~)"},
  N = List.Count(Source),
  Subsets =
      List.Transform(
          {0..Number.Power(2, N)-1},
          (i) => List.Transform(
                     {0..N-1},
                     (j) => if Number.Mod(Number.IntegerDivide(i, Number.Power(2, j)), 2) = 1
                            then Source{j}
                            else null
                 )
      ),
  Concatenate = List.Transform(Subsets, each Text.Combine(List.RemoveNulls(_), ""))
in
  Concatenate

Output: