Not sure it will fit your criteria, but here are some other shows I could think of (not always treated in a realistic way though):
- Freeter, Ie wo kau : how to buy a house when you're working part-time
and on the same topic : Princess Maison
- adoption (from a teenage mother): the movie True Mothers
- raising an impaired child (it's somehow a cohabitation show but it's more than that) : Kiseki no Hito
- taking care of the deceased and their family : the wonderful movie Departures or the family business drama (but also mystery genre) Saikou no Jinsei no Owarikata
Japan is also pretty good at making dramas anticipating social issues consequences (and how to solve it - dystopian dramas):
- declining marriage rate: Kekkon Aite wa Chusen de
- environmental issues: Nihon Chinbotsu: Kibo no Hito
And of course you've got countless of dramas centered on illnesses, or on jobs (and not always the most known ones like cook in a school, supermarket employees, healthcare employees...)