Once the menu is up, your game will pause and you’re free to start all the crazy shenanigans your heart desires. Plug it back in after and you should be able to seamlessly use both at once.
If you’re playing with a controller, there’s a chance that won’t work, so just unplug your controller first, then press it. Pressing the tilde key (~) should bring it right up. To input a console command you just need to bring up the menu.
