TNG tried doing stuff with the characters. Data got the emotion chip. Riker and Troi got together.
Picard lost his brother and nephew. Geordi traded in his VISOR.
Dr. Crusher..... Dr. Crusher... er, um...
Those are plot events. DOING something with a character means doing something dramatic: making the character have to solve problems or make a choice. Of the above list the only ones that meet the criteria might be Picard DEALING with the deaths in his family, and Data DEALING with his newfound emotions.