The only program I've come across that can do this is 'Quicktime 7 Pro' on the Mac (not Win). In QT7 pro, you go to preferences and select 'Native Device' this will record uncompressed video and audio together with as many inputs as your Audio interface has. You then export the audio (PCM) and open it in a DAW and all the tracks are there. Only problem is that you can't choose the amount of tracks (it uses ALL the inputs of your interface) so I have 26 tracks and end up deleting 22 of them, leaving me with the 4 I used for audio. Then you can do your edit, mixes etc, add it back to the video file (in QT7 pro again) and you have your finished video. This is not for streaming obviously, but it's the only program I've ever come across that can record Video AND multiple audio tracks at the same time. Incredible that in the last 25 years nobody else has figured out how to do it......