There are a few factors in this situation.
You can use the max number of overlays according to your subscription plan but in stream can be used only one at the time because of the websocket(*).
Via Controller you can change which overlay to use and that’s it.
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* websocket – especially to overlays which need to read tips (like tip alerts) are “heavy” on user’s device (because there must be an additional connection between Chaturbate for example and user’s overlay to read the tips and trigger the animation/alert)

Anyway, I will talk to lead developer and see if we can enable multi-overlays, at least for categories of resources which don’t use tip alerts but I can’t promise anything.
An overlay runs from a single URL (browser based URL), so all saved overlays of the same user run from the same URL… content is changed but the url is the same.
Your suggestion implies multiple URLs, different URLs for each saved project.
That’s my logic tho I’m not the developer, just the designer.

@Bellablackthorne , thank you for your suggestion.
We’ll see what can be done and get back to you.