Cool idea.
Combos are tough. There are different ways to accomplish the task.
Luckily, we software engineers are great at it. This is called a design decision. First you have to determine a start point and end point.
For example? In a battle, when someone wins, what do they get? Additional attributes, statistical information, like a win/loss?
Another important thing to remember is any kind of battle system helps the player achieve larger goals in the game, whether it may be gaining experience or preparing for tougher levels, and/or combination, or obtaining money for better equipment,etc...
The end point determines what the gamer's get out of the battle, so you should design it to do multiple things that improve the situation of the player. The duration of the battle is also important.
Also, if you want battles one after another, that is called an "arena" game or mode, side quest or side mode module for an rpg or free explore game. To make an effective "system", like I think you are trying to do, you would design the user interface with that in mind, so players will enjoy it more.
As far as how you implement the system, what moves you create, is determined by characters, game play style, theme, etc...
There are multiple keywords there for you to research and explore. Hope that helps!!