Gohan's character often develops by learning to control his Super Saiyan 3 power better. He might start out as a bit reckless with it and then grow more disciplined. For example, he could initially use it to show off but later realize the responsibility that comes with such great power.
One common theme is adventure. Since Gohan has his Beast form, they might go on adventures together fighting enemies. Another theme could be romance, exploring their relationship deeper.
Gohan could become more of a leader. With the power of Super Saiyan 5, he would be one of the most powerful beings in the universe. Other Z - fighters might look to him for guidance and leadership. This could bring out a more assertive side of his personality. He would need to step up and make tough decisions for the greater good, which would shape his personality in a more authoritative way.
One idea could be Gohan in his Super Saiyan 4 form facing a new, powerful enemy from another dimension. He could struggle at first to control the raw power of this form while also trying to protect his friends and family. Maybe this new enemy has the ability to nullify the Saiyan's energy attacks, forcing Gohan to rely more on his martial arts skills that he learned from Piccolo.
In a fanfiction, Gohan as Super Saiyan 3 could be involved in a time - travel adventure. He travels back to a crucial point in Dragon Ball Z history and has to use his Super Saiyan 3 powers to change certain events. This could lead to a whole new timeline where things are different. For example, he might be able to prevent the destruction of Planet Namek or save some characters who originally died.