The primary source of power in Adventures in Oz is friendship. As characters explore Oz and make friends, they become increasingly powerful.
It can be a problem when every character goes on every adventure and makes every friend available to them. Not only will they be the exact same power level (which is not bad), they will be very much the same character because they followed the same advancement path (which is bad). In order to make sure that "spotlight moments" are distributed evenly, you have to ensure that players are not competing for the same spotlight. If the answer to a challenge is a cookie and everyone has Cayke the Cookie Cook on their Friends List, the only real question is who speaks up first.
There are a couple of solutions to this problem, which I should make a point of including should I do a revised edition of the game.
1) Keep at least some friendship opportunities simple/individual. In The Wonderful Wizard of Oz, the Tin Woodman is the only one who acts to save the Queen of the Field Mice from the bobcat. so he's the only one who can call on her aid. Throughout the stories, it is usually a single character helping another, though which member of the party helps in which case is what makes it an ensemble story.
2) Encourage troupe style play. This is another nod to the structure of the original stories. Dorothy, Scarecrow, Tin Woodman, the Cowardly Lion and Toto never adventure together again in that specific arrangement again. The closest it comes to happening again is in Ozma of Oz, with only Toto missing from the ensemble, but also includes a significant cast of new characters, such as Tik-Tok and Billina. So even if everyone playing in one adventure gets to add Cayke the Cookie Cook to their Friends Lists, the next session may include only one or two of those characters, keeping variety high.