Is there any open source software available for a Raspberry Pi that will read multiple camera streams on the local network and rebroadcast, keeping them as separate streams?
This will very much depend on what cameras you are using and what protocols they support and where you want to send the collection of streams.
For example I have 2 camera's that support ONVIF which means they have RTSP feeds. I can then use something like ffmpeg to restream as RTMP to NGINX which in turn converts them to HLS/DASH that can be viewed in a browser or streamed to something like a Chromecast.
The depending which video codex the cameras use will determine how hard ffmpeg needs to work and this is likely to be the limiting factor on a Raspberry Pi.
The cameras are both on my private lan and the NGINX machine is exposed to the Internet so I can check on them when away.
The following post on my blog has some more of the technical details: https://www.hardill.me.uk/wordpress/2020/05/03/streaming-camera-to-chromecast/