This question occurred to me, which seems at first glance relatively easy to determine, but actually becomes very complex when you consider capturing, ko fights, handicap stones (ignoring handicap komi which is arguably infinite), etc. No doubt the ruleset has significant impact here too!

I will offer my “Fermat’s Theorem”, that a score over 361 is possible for a single player, and moreover I suspect over several thousand can be obtained (though my knowledge of the rules is functional at best).

Anyway, mathematicians and pedants welcome.