I think it is important to keep the basic counter of cavalry versus archers versus infantry. But then within each of those groups there can be another Rock-paper-scissors system. Slingers versus javelins versus archers. Swordman versus spear and pike versus ax or club. Another way to look at each group is one unit is most specialized, for instance the slinger is the best at killing infantry but the most vulnerable to cavalry; a second unit is somewhat all purpose or resistant to the basic counter, for instance javelin throwers could be less vulnerable to cavalry than other range units and swordmen could be better against archers than pikemen are.
I would avoid using artificial counters; I prefer the type of armor and attack a unit has making it happen naturally in most cases. If the javelin infantry has high pierce armor and low crush armor it will naturally be good against archers and bad against slingers, for instance. That would be an especially useful change in A23 since it would make the foot javelin a counter to the javelin cavalry, who is currently good against just about everybody. I'm making a mod to implement these ideas.
