Can I go back to last year's class composition, by just shifting one level?

Yes. To assign students to classes based on the previous year's classes, go to the display Timetable > Students > List, sort the list in the column Cl. prev. yr. (Previous year's class), select all students in a class, right-click and activate the command Modify > Class: In the pop-up window, double-click on their new class.