I’m having a similar issue. Running in editor/PIE is fine where it creates a new client that auto-connects to the main game (brownie points if someone can point out which source file allows this magic), but after packaging it, I can only run one instance. I can open a second instance for a split second before the first shuts down.
I can get around this issue by running the program as another user (Windows 10) and then running it again as myself so I have both windows open at the same time on my screen, but it feels janky and kind of hacky, so if someone has a better solution, please let us know.