hi.
you can do this with OBS, just keep it mind it's an experimental 3rd party add-on. it's not harmful, just not polished or complete.. and could cause issues/errors or could be just fine.
homepage: https://sorayuki.github.io/obs-multi-rtmp/ The page is written in Japanese because it's a plugin originally build for vtubers. This is a plugin to streaming to multiple RTMP servers concurrently. It's able to share encoders with main...
obsproject.com
you need to make sure your computer can handle encoding the streams multiple times, if they are requiring different settings per site...
another option you have is using an RTMP service, there are a few available at various price ranges... i am not going to recommend any because i don't know them (also, perhaps soon i will be able to provide this service to some, but if i knew of one i would mention; google search if you like RTMP provider)
a few of the models on here will recommend Shinemodel, find it from google search, and they will vouch for it.. it uses a chromium browser to house all your stream chats and webcam output to the sites... using an RTMP service they provide free of charge.
just read over and understand the privacy policies on anything you sign up for online is the best advice i can give.
hope this helps!
-l
edit:
here is a direct link to the obs-multi-rtmp
https://github.com/sorayuki/obs-multi-rtmp/releases/
consult README and download .ZIP
this software is all open source, just like OBS