If you graduate, you may move along to middle school. Middle school is honestly boring. You can be a tad more mischievous by leaving gum on the hallway floors in order to trip your opponents during the physical battles. You have a few new choices in your classes, and a few other new options. There would also be fewer bullies.
High School is where things get bloodier. School sports begin and you can take down your opponent on the field, and you can choose your classes. Choose more than 3 science or other specialized classes together and you get "super powers", or spread your choices out and have some art, some science and some language etc.
Your specialized classes will give you new weapons. If you choose sculpting classes, for instance, you can use your skills in sculpting to fool your opponent, challenge your opponent, or inhibit your opponent. However, you could also use your chisel to stab your opponent during the bloodier battles. If alongside sculpting, you took a painting class, you could paint your opponent onto another scene, or a hole beneath them etc. You can fight them physically with your paintbrush or use the paint to slip them etc. You could also now paint a better scene with the addition of your sculpting abilities, because now it can be 3-D. If alongside all of that you took digital filmmaking, you could embarrass your opponent in their confusion or document the situation and earn a little cash on the side.
If you chose science classes, you might attack with labratory equipment or sick your pet rat with experimental rabies on them.
Naturally the classes will become more complicated and get better weapons if you graduate High School (if you lose too many battles you can flunk, and depending on your grade, you might get into a better or worse University). If you graduate, you go to college and from there you can choose from majors and you don't have to answer any more general education unless you choose the classes. As a film student, for instance, your weapons outside of the gen ed weapons, would all be specialized towards film. You can get a Xenon light and blind your opponent or burn them, or steal their soul with the camera. As a programming student you can reprogram specific traits of your character or your opponent during each battle. Of course, you'd actually have to know how to program. As a creative writing major, you would be able to defeat your opponent with the fanciest words you can think of - the fancier the better. If you say "disintegrate" for instance, that would be an intermediate word and would do a mediocre job of destroying the enemy, while "obstinate" might slow their abilities for a longer period of time. "Matriculate" would be a fantastic word to use on yourself.
I imagine all of the characters would look a bit like Scott Pilgrim people or anime anyway. The main goal is to graduate college. "Smart" battles would take place in the classrooms, where you have to use your weapons in the way they were meant to be used and out-do your opponents. Outside of the classroom you can also challenge opponents to "smart" battles, though in college it would need to be within your major or their major. Physical battles would take place at recess, at lunch, in the parking lots, and in the hallways. You can use whatever weapons you have in your backpack. That would include textbooks, computers, phones, pencils, pens, chisels, cameras, test tubes, paint, lighting gear, running shoes, and anything that might have to do with whatever classes you are taking at school.
An example of a physical university level battle:
Chemistry major vs Culinary major
demented lab rat
broken test tube
Students would face each other in their location. First the chemistry student may spray acid towards the culinary student. The culinary retaliates by shoving out the wedding cake to absorb the dangerous substance, and then toss a bit of silverware towards the chemistry student. The chemist would then block this with the heavy textbook and set loose the demented lab rat. The cook may then trap the rat with the mixing bowl or kill it with the spatula or butcher knife if they think they're good enough at using it. They could also poison the rat or get it drunk. Their next option might be to toss their butcher knife. At this point the textbook may be too weak to defend, depending on how the silverware attack went earlier. If the butcher knife went through the chemistry student would flunk his course, or be given a warning by his teacher and the culinary student would move on to the next round.
Another example is of a Creative Writing student versus a Music Major.
Music (stringed instruments)
sleep-inducing sheet music
In this situation we will pretend like the music major strikes first. First they might attempt to set their opponent to sleep by playing their song, but before this is able to kick in, the creative writing student might say "excite me" and the music would pick up a bit. If they used a word like "galvanize" they might do better in that defense. This would be the writer using their dictionary in defense. Next the creative writer might attack by describing as detailed as they can, a hole beneath the musician. The musician might then use the strings from one of their musical instruments to tie a rope to the ceiling. They might then shoot guitar picks at their opponent. The writer could block these using their fictional book or their imagination. They might next launch their pencil into the string and break it. The music major swings over before the pencil hits and swings a guitar at the writer, who blocks this attack with their notebook.
Anyway, you get the idea. Different majors would have different kinds of fights. So basically, the game would be an epic all-out war between the students at your school. It is not only a battle of random skills, but of wits! The more you know about your subject the better you could do. The best thing ever is the expansion packs - Battle Students: Demolish the Greeks (fraternities and sororities) and Battle Students: Jocks vs Nerds. There could also be Battle School: Master's Degree and Battle School: Extra-Cirricular