Can I store soft serve ice cream in my regular freezer?
The standard recommended temperature for a home freezer is 0°F (-18℃). Regular ice cream keeps best at -5°F to 0°F. However, the proper storage temperature for soft serve ice cream is 18°F (-7℃). 

While you could raise the temperature of your freezer to accommodate this, it really wouldn't be recommended for the rest of your frozen foods.

Short of that, your best option would be to get a tiny freezer just for your soft serve so that you can keep it at at higher temperature without risking the quality of your other food.