Set up a different Profile and Scene Collection for each independent stream. Put the relevant key in each, set up the sources, etc. If they're similar, it might be good to set up one of them, then Duplicate to make the others and modify from there.
Be aware though, that some operating systems still have exclusive access to media sources. Historically, that was done for performance reasons, and not all OS's have relaxed it yet. If you're on one of those, then you can't use the same camera in more than one instance of OBS, or in another app and OBS, at the same time. There might still be a creative way to make it work though, possibly using the Virtual Camera from one instance of OBS to another, or one of the direct OBS-to-OBS plugins.
Anyway, once you have a different set of settings for each session, you can specify on the command-line, which one to load, and to not complain about multiple instances:
obs --multi --profile "Exact name of profile" --collection "Exact name of scene collection"
You can copy a shortcut or desktop file, or whatever your OS calls it, and modify the command line in there, or you can make a script that does all of them with the appropriate timing and order along with everything else you're doing, in case that matters.
obs --help in a terminal (Command Prompt for Windoze), to see all that you can do there. :-)
