Custom Column for Multiple IF & And Statements

If I understand your logic correctly, this should work:

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WcvJx9PM2VNKBMIxgDGOlWJ1opRCQBIyAC+BUCZfAqjrECMlMNO1wV+CXgJqL6WYMs0OwageqigUA", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [AST1 = _t, AST2 = _t, AST3 = _t]),
    #"Added Custom" = Table.AddColumn(Source, "Custom", each
        let
            L = List.Distinct(List.Select({[AST1],[AST2],[AST3]}, each not Text.StartsWith(_, "BLANK")))
        in
            if List.Count(L) = 0 then "Investigate"
            else if List.Count(L) > 1 then "House"
            else L{0},
        type text)
in
    #"Added Custom"

This takes the list of values in AST1, AST2, AST3 and removes the items starting with "BLANK". Then it removes any duplicates and returns different values depending on how many items remain.