Given two sets of items then if any item is common to any set then the result of applying consolidation to those sets is a set of sets whose contents is:

 The two input sets if no common item exists between the two input sets of items.
 The single set that is the union of the two input sets if they share a common item.

Given N sets of items where N>2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible.
If N<2 then consolidation has no strict meaning and the input can be returned.

Example 1:
Given the two sets {A,B} and {C,D} then there is no common element between the sets and the result is the same as the input.
Example 2:
Given the two sets {A,B} and {B,D} then there is a common element B between the sets and the result is the single set {B,D,A}. (Note that order of items in a set is immaterial: {A,B,D} is the same as {B,D,A} and {D,A,B}, etc).
Example 3:
Given the three sets {A,B} and {C,D} and {D,B} then there is no common element between the sets {A,B} and {C,D} but the sets {A,B} and {D,B} do share a common element that consolidates to produce the result {B,D,A}. On examining this result with the remaining set, {C,D}, they share a common element and so consolidate to the final output of the single set {A,B,C,D}
Example 4:
The consolidation of the five sets:
{H,I,K}, {A,B}, {C,D}, {D,B}, and {F,G,H}
Is the two sets:
{A, C, B, D}, and {G, F, I, H, K}

See also

 Connected component (graph theory)
 Range consolidation


Private Function has_intersection(set1 As Collection, set2 As Collection) As Boolean
    For Each element In set1
        On Error Resume Next
        tmp = set2(element)
        If tmp = element Then
            has_intersection = True
            Exit Function
        End If
    Next element
End Function
Private Sub union(set1 As Collection, set2 As Collection)
    For Each element In set2
        On Error Resume Next
        tmp = set1(element)
        If tmp <> element Then
            set1.Add element, element
        End If
    Next element
End Sub
Private Function consolidate(sets As Collection) As Collection
    For i = sets.Count To 1 Step -1
        For j = sets.Count To i + 1 Step -1
            If has_intersection(sets(i), sets(j)) Then
                union sets(i), sets(j)
                sets.Remove j
            End If
        Next j
    Next i
    Set consolidate = sets
End Function
Private Function mc(s As Variant) As Collection
    Dim res As New Collection
    For i = 1 To Len(s)
        res.Add Mid(s, i, 1), Mid(s, i, 1)
    Next i
    Set mc = res
End Function
Private Function ms(t As Variant) As Collection
    Dim res As New Collection
    Dim element As Collection
    For i = LBound(t) To UBound(t)
        Set element = t(i)
        res.Add t(i)
    Next i
    Set ms = res
End Function
Private Sub show(x As Collection)
    Dim t() As String
    Dim u() As String
    ReDim t(1 To x.Count)
    For i = 1 To x.Count
        ReDim u(1 To x(i).Count)
        For j = 1 To x(i).Count
            u(j) = x(i)(j)
        Next j
        t(i) = "{" & Join(u, ", ") & "}"
    Next i
    Debug.Print "{" & Join(t, ", ") & "}"
End Sub
Public Sub main()
    show consolidate(ms(Array(mc("AB"), mc("CD"))))
    show consolidate(ms(Array(mc("AB"), mc("BD"))))
    show consolidate(ms(Array(mc("AB"), mc("CD"), mc("DB"))))
    show consolidate(ms(Array(mc("HIK"), mc("AB"), mc("CD"), mc("DB"), mc("FGH"))))
End Sub