Supporting characters fill in a variety of roles. They can be the love interest, the comedic relief, the sidekick and so many others. They don’t just support your protagonist however, they also provide aid for your antagonist.
Figuring out the reasons your supporting characters aid your heroes and villains helps flesh out their character as well as helping give strength to their relationships with each other.
As an exercise: Write a list of your supporting characters. Label or highlight the ones that could support your antagonist. Why could they? Write a scene explaining why they do or do not support him. Do the same thing for any characters that could support your protagonist.
Take a look at your list. Are there any characters that could play for both sides? Write a scene where they decide one way or the other who they’ll follow.