Co-sanctioned events

Most clubs I know of have, in the past, only held NRA sanctioned 900/1800/2700 Bullseye matches. Therefore most shooters typically only have an NRA Classification, unless they shot at Perry and Cardinal in the past two summers and have a record with CMP.

If my memory serves, for the 2021 Perry (and Cardinal?) everyone just used their NRA Classification.

I have been told that NRA Classified shooters can elect to take the same classification for CMP matches as long as it is at or above whatever record they have (if any) with CMP, although I must say that I did not notice that option on the 2022 registration forms (probably my oversight).

In an ideal world everyone would have uniform NRA and CMP Classifications and we would all be on a "level playing field".

So, now my question, can clubs choose to run a match sanctioned by both NRA and CMP? 

I realise that this would entail two lots of fees and paperwork, that might not be palatable to many shooters or match directors, but if indeed it is permitted, some shooters might choose to do this in order to establish their proper classification in both camps.

At the particularly well organized Auroroa Sportsman Club bullseye matches in Waterman, Illinois, for 2022 they offer submitting scores to either one (NRA or CMP) but not both. The match fees differ between bodies.

I thought about this earlier in the year when I took over running my club's matches. I decided against for the following reasons
1.) CMP and NRA have different sanctioning fees, to have both I could either pass on the cost to the shooter or minimize the funds available to upkeep the range and the equipment at the club
2.) Rule books are similar, but different and could conflict in some areas, not ideal from an officiating perspective
3.) additional paper work

I think (correct me if I am wrong) the main concern is about shooters who have a higher NRA classification than CMP and the appearance of sandbagging the CMP sanctioned matches. To this I would like to offer this perspective, If for example an NRA Master, has only achieved a CMP Expert or less and does not opt to shoot under the higher classification, they are doing so at their own detriment and are limiting their performance by mentally accepting that they only have to perform at the lower level. 

Just my opinion on the matter. The group of shooters is small enough that it will become clearly evident if someone is trying to game the class system long enough, at some point or another they will be called out on doing so.