If I recall correctly the way it works is that ZnT mages have two factors to consider when learning/creating spells.
The first is what rank they are capable of casting at. Each rank has a number of slots corresponding to the number of dots required to draw it. So dot spells have one, line two, triangle three, and square four. Into each of these slots an element can go.
By stacking multiple copies of the same element you can create a more powerful effective, for example a fireball with one Fire element will be small and weak while one with four would be large and incredibly hot, while mixing different elements together will create different effects.
An example of this would be Tabitha's Ice Spears; they are a Triangle rank spell because first she must create the ice (Water + Wind) then propel the ice (Wind) for a total of (Water + Wind + Wind). Later on when she hits Square rank Tabitha improves her Ice Spears by increasing the speed (Wind) for a total of (Water + Wind + Wind + Wind).
The second factor to consider is their skill with the elements. No matter how high their rank a mage is still limited by their skill with each given element. So even if you are a Square rank mage your not going to pull of Square rank Fireball (Fire + Fire + Fire + Fire) without some serious skill in fire magic.
This is why the majority of mages you see are specialized in either one or two elements; because it's just not worth training up their affinity with the other elements when they can instead get greater returns by focusing on improving their skill over the element/s they are already good at.
That is what will make Gamer!Louise utterly terrifying. Because thanks to the insane rate at which a Gamer can grind their skills I wouldn't be surprised if she could hit Square rank in all four elements.
