Thanks. From what I can see, I cannot put what I want in the "Max Players" or "Cooperative" field in the shared database. I can put what I want in the "Play Mode" field that I can access in my local database, which would be a non-trivial task to perform and would not be made available back to the cloud Launchbox Games Database, meaning ultimately any effort would not be shared with the community. Finally if there was a way to upload it back to the cloud (that I'm unaware of), then entering free text like this into such a field would ultimately end up with a whole range of non-standard, inconsistent terms being used which could make the effort in vain anyway.
A "Multiplayer Modes" field that only allows certain values in the cloud Games Database would solve many of these problems, and implementation of https://bitbucket.org/jasondavidcarr/launchbox/issues/285/additional-scraper-options by scraping Co-Optimus (or similar) would be a great way to sourcing the required information rather than manually entering it.