Yes, a student can be in more than one class at a time. Each teacher will be able to see the student in their class and on their reports if a student is in multiple classes.
Each class can have a separate list of assignments. When students log in, they can choose which class's assignments they want to play.
Student's can only have one grade-level Journey at a time. Any teacher with access to the student can change their Journey.
If you're in a school that is rostered, the data table that is sent to ST Math has to list additional teachers as co-teachers. Check with your school office for more information.
If your students use picture passwords, you can add any student to your class either by using an Invitation Code or by searching for the student. The instructions are the same as for transferring students and can be found in this article: How do I transfer student to a different class?