OS/VS COBOL, COBOL II, Enterprise COBOL for z/OS. OpenCOBOL and OOCobol.
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I think you misunderstand -- it is not that they are not allowed. It is very possible to generate a table with duplicate key values and use that table in a SEARCH ALL statement. What IBM tells you is that, if the keys are not ascending (or descending, depending upon the coding) -- and duplicate keys are definitely not ascending (nor descending) -- then you CANNOT be assured that the SEARCH ALL worked. It may return a wrong record, or it may fail to return a record even though the key is in the table.