tl;dr: You can fork the Signal code if you want, but if you do, Moxie Marlinspike asks you to change the app name and run your own servers. The server source code appears to be available at https://github.com/WhisperSystems/Signal-Server, but I've heard it doesn't include the voice component.

So, for example, if you think that Signal ought to support a feature like iMessage's "Invisible Ink" (https://mic.com/articles/146347/i-os-10-s-invisible-ink-feat...), which Moxie has specifically refused to support (https://github.com/WhisperSystems/Signal-Android/issues/5103), then you can't just fork the client, implement it yourself, and use the new client normally, because you'd no longer be able to talk to regular Signal client if I understand correctly. I mean, even if you figured out a way for two clients to tell each other whether or not the feature was available.

So Signal is open source, but not in a way that's useful if you want to change something.

I don't want to discourage people from using Signal. It's a great app. But I thought this was worth pointing out, assuming the LibreSignal is representative of what will happen if people want to make changes to their client.