it is possible to get supplementary benefits (“supplerende dagpenge”) in case you have a part-time work together with receiving Unemployment benefits (“dagpenge”). However you must be available for FULL-time job while receiving supplementary benefits, meaning that you must apply for full-time jobs.
Its also a requirement that you can quit your current part-time without notice-period, i.e. you must be able to stop from day to day in your current part-time job. This is because you must be fully available for the labor-market, for being eligible for dagpenge.
Furthermore there is a limit of maximum 30 weeks where you can receive supplementary benefits. After that you must decide whether you want to keep your part-time job (and stop receiving dagpenge) OR you want to stop your part-time job (and go on full dagpenge).
If you think supplementary benefits is an option for you, then you must be approved for this in you A-kasse.
Graduates as well as wage-earners can apply for and get supplementary benefits. However for graduates the benefits amount (dagpengesats) is lower.