There are ways to do that, but they tend to get kinda messy. My general philosophy is that each set of content requires its own instance of OBS, and you can have multiple instances running on the same machine if you use the command line and give each one the right options.
obs --help
in the Command Prompt to see all that you can do there. :-)
I use two instances myself, to run a meeting that has both local and remote participants. One produces the feed to the remote people, just like any other livestream, and the other takes the virtual camera from that and a window-capture of the meeting, and produces the local display and recording. The Advanced Scene Switcher plugin automates everything, so I only have to think about the "livestream", and everything else "just happens".
This plugin will allow you to automate various tasks using "Macros". Macros consist of a list of conditions under which a list of actions will be performed. Examples and guides can be found in the wiki. Feel free to contribute! If you run...
obsproject.com
The master instance has a naming convention for the scenes, so that Adv. SS knows what WebSocket message to send for each one, and the slave instance receives those WebSocket messages and does its thing accordingly.
I have a script for that rig to keep it all straight; there's no way I'll remember everything every time!