Yes, working students ("Werkstudenten") in Germany can be insured under Private Health Insurance (PKV)
like Study Secure Premium by ottonova, but there are important conditions to consider.

Important: Both publicly and privately insured students can work during their studies, as long as they
maintain their student status.

Here is a quick breakdown of the hours you can work while maintaining your student status (as of 2025):

• Up to 20 hours/week: You keep your student status and can stay on your Private Insurance.
• 26-week rule: You may work over 20 hours/week for up to 26 weeks per year if it’s during semester
  breaks, evenings/nights, or weekends.
  
  If you work more than these hours, you will lose your student status and instead become an employee.
  This means you must switch to Public Insurance (GKV).
  It is important that you follow these working hour limits so that you do not breach the terms of your visa.

Does my employer have to pay any additional costs for me as a privately insured working student?

No, there are no additional costs for your employer compared to publicly Insured working students.