You will have 3 characters to play, and they all start at a "base" class. There are 4 classes into which a character can change to learn new skills and magic, and also an ultimate class (called here "attainment" class).
In many other Kemco games, if you do enough grinding you can change to and master every class. There are constraints in Chronus Arc that make this impossible without items from the IAP shop. There are two conditions required for change: the character must be at least level 30, and you must have a "document of discipline." This document is consumed during the change process.
There are only 6 "documents of discipline" available outside the IAP shop, so you cannot have all characters master every class. The "attainment" class requires a character to have mastered all 4 classes and have a "document of attainment" of which there are only 2 in the game (plus one in the post-game after defeating the final boss).
You master a class at level 30, but there are some classes that have special skills or magic that are not obtained until after level 30 (see the lists). In that case you may choose to defer the class change until you learn the skill.
When you change classes, you retain all the special skills and magic you have obtained, but your level goes back to 1 in the new class. When you change classes and return to level 1, it is possible you will see a large reduction in your stats. Don't panic--the level rise is significantly faster than in the base class. In fact, the ultimate stat increases from class changes may be more valuable than the new skills to be learned.
Since you cannot master every class, you will need to examine the lists carefully to decide on each change. Although many of the skills/magic are common across characters, there are some that are unique. You probably will earn enough points for the IAP to purchase a few additional "documents of discipline."