Co-op Mode meta can drastically change between player amounts and comps (some bosses strats change with more players because bosses will cast more copies of a skill) so Id like to propose 3 player based categories and then 3 subcategories thereof:

Main Categories: Co-op 2P Co-op 3P Co-op 4P

Sub-categories: All Same (AS) No Same (NS) Some Same (SS)

Sameness depends on team comp. All Same would be like Necro x Necro x Necro on 3P, Some Same would be like Necro x Necro x Whitemage, while No Same would be like Necro x Whitemage x Pyromancer

I'm not 100% sure how speedrun categories work or if these could just be added as filters, but the sheer speed difference of runs between player amounts may make it worth doing entirely separate categories.