find Sum of # of days w/o counting overlapping days twice with multiple paramaters

civ1979, you may try running this on your worksheet.

Sub a()
    Dim dic As Object, i As Long, d As Date
    Set dic = CreateObject("scripting.dictionary")
    dic.comparemode = 1
    
    Application.ScreenUpdating = False
    
    For i = 2 To Cells(rows.count, 1).End(xlUp).row
        d = Cells(i, 4).Value
        Do While d <= Cells(i, 5).Value
            If d >= Cells(i, 1).Value Then
                If Not dic.Exists(Cells(i, 3).Value & "_@_" & Format(d, "ddmmyyyy")) Then
                    dic.Item(Cells(i, 3).Value & "_@_" & Format(d, "ddmmyyyy")) = 1
                    Cells(i, 6).Value = Cells(i, 6).Value + 1
                End If
            End If
            If d = Cells(i, 5).Value And Cells(i, 6).Value > 0 Then Cells(i, 6).Value = Cells(i, 6).Value - 1
            d = d + 1
        Loop
    Next
    
    Application.ScreenUpdating = True
    
    dic.RemoveAll
    Set dic = Nothing
End Sub

There are some ambiguity, especially for those where start and end dates are the same day; should that be 1 or 0 days?