One interesting storyline could be about the discovery of long - lost Potter family secrets. For example, a hidden magic that was lost for generations but is now being rediscovered within the protected walls of the Potter house in the fanfic. Another could be the training of a new generation of wizards by the Potter family, with unique spells and magical techniques being passed down.
Well, in some fanfics under this theme, there might be a storyline where the Potter house becomes a sanctuary for magical creatures. The Potters protect these creatures from dark wizards who want to use them for evil purposes. It could involve the main characters learning about the unique needs and powers of these creatures while defending them.
There could be a story where the Potter family under the protection of their house has to deal with a time - traveling threat. Enemies from the past or future try to change the course of the Potter family's history. The family has to use their knowledge of magic, as well as the special protections of the house, to fight against this threat and preserve their family's legacy.