Multiplayer friendly scoreboard inventory

For a roguelike/lite map:
Current Idea:
Whenever you pick up an item it gets /clear 'ed and /scoreboard players add  player1Items 1  (All items stack)
Any ideas on how to optimise this so it works for multiple people having different "inventories" without creating 10 scoreboards and keeping track of which player owns a scoreboard?
Doesn't need to be a command just a general idea that I can /execute