Hey @TheBatgirlofNML! 
Thanks for reaching out about this.
As long as the game stays within the official DC Community Guidelines, this should be fine. Here’s an interesting thread where other community members discussed setting up something like what you are describing: Discussion and Interest Check: DCU RPG Group
I recommend running your idea through us (the moderator team) via direct message once you get your thoughts more fully fleshed out, and we can help you further in bringing your vision to life! 