Yes, students can have access to as many different classes as they want under their account.
When students log in at account.tytoonline.com to manage their own accounts, they are shown a list of classes they are part of. At the top, they have an easy way to add a registration code for a new class.
After the student enters a code and selects "Register" the page will let them know if it was successful, and add the new course to their list.
Now, when a student logs into Tyto Online (the game), it will show them a list of Classes they are part of, and ask them to choose which class they want to play under. If you want to read more about the experience for students who are part of multiple classes, please read the help article on that!