Not if the upper-level courses have prerequisites, which is typically the case in STEM programs. In my EE program the courses were scheduled so that it was impossible to graduate in less than four years. Most courses beyond freshman year had only one or two sections, taught during a specific semester.
At my university in the EE program you had to complete all freshman and sophomore level classes before you were allowed to take any junior or senior level classes.
You also had to meet with an adviser towards the end of each semester before you were released to schedule classes for the next. Apparently engineers tried to circumvent the rules too many times, probably because we're always focused on optimizing solutions.
You can be taking freshman-level courses your senior year.
Or, if you are up to the challenging, junior level courses your freshmen year.