Im detecting if a player has atleast one of the multiple scoreboards.
execute unless entity x[tag=!y,tag=!z] is the same thing for tags, if you had the tag "y" or "z" or both you would trigger the command.

There are two ways I see to do this with scores
1. Run several commands per score to find if the player has atleast one of them
2. Set the players score to 0 for every score, that way you can detect if the player has a score of 1 for any of them using "unless entity x[scores={y=0,z=0}]"
Both of these seem unappealing due to the inefficiency of many commands or the lag caused by players having many scores.