Been working on this one. It is challenging.
I have about 3 variations on one approach that treats 2 matching/3 matching/4 .... etc separately and you will likely want separate sheets (workbooks?) for each. They are all array formulas. Using these on 1,000 rows (20-30 columns of output) will take a l-o-n-g time to calculate if Excel can handle it at all. I have not found a work around for that. It will also create file bloat.
I have another that returns all matches greater than 1, but it doesn't organize in an informative way. i.e. they are not grouped according to 2 match, 3 match etc. So far I have not found a work around for that either.
Please let us know which output you favor.
RE: the performance hits and file sizes. For those reasons I don't recommend any of these. If some one else doesn't come up with acceptable formula solution you might want to consider asking a Moderator or Administrator to move this thread to the VBA or Pivot table(?) sub-forum. VBA/Pivot may have tools to handle the logic more efficiently. Please do not do this yourself. That's called double posting.
Please see the attached. There are 5 sheets. 'MATCH-MODE.MULT', 'COUNTIF-MODE.MULT', 'MATCH-MATCH - 2', 'MATCH-MATCH - 3)' and 'MATCH > 1'.
The first four have 2 helper rows and a helper cell. The fifth one does not. The MATCH-MATCH ones perform noticeably faster.
The formulas (array entered) in Sheet order are
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