Yes you can. In fact, any global variable is local to the client only, unless a publicVariable command is used to synch it, or a trigger with appropriate conditions synchs it. A variable with the same name can have different values on each client, unless you make an explicit attempt to keep them in synch.
Let's say you place a trigger on your map with the condition field this and ({local _x} count thisList) > 0
This trigger will only fire on the machine of the player who is in it. It effectively behaves as an independant trigger for each player.