USB from 2 PCs into 1 DAC? Possible?

Looking for a way to connect USB from 2 different PCs into a MiniDSP 2x4HD.

My use case-

I work from home and have 2 Windows machines at my desk.

The first is a work laptop which is connected to the 2x4HD via USB and that connects to a 2.1 audio system.

The second is a mini PC for personal use which is connected to a TV as the monitor and I've been using the internal speakers in it for now.

I'd love an easy solution to connect both machines to the 2x4HD via USB, if this is even possible. I haven't tried yet, but I'm guessing a USB hub would not work as there would be conflicting hosts?

Any thoughts?
 
I should expand on what my actual needs are-
1. I need both PC audio sources to be available simultaneously, not have to switch between them
2. My audio sources will be streaming apps, i.e. Spotify and YouTube from one PC, and video calls, i.e. Teams and Zoom from the second PC.
 
Unless I'm missing something, that also won't work as the inputs on the MiniDSP are switched and only 1 input type can be active at a time.

Pretty sure what I need does not exist so I'm currently looking at USB DACs and I'll combine the analog signals from both PCs into 1 stereo pair.
 
If I understand correctly, you could probably find a DAW that can combine the analog out of the minidsp with the usb signal from the pc the DAW is attached to. Would save an anlog mix following the usb dac/minidsp. One other option might be possible, which is feed the analog out of the non-minidsp PC to the analog in of the minidsp PC and combine the signals on the PC. Assuming the PC's have analog in/out.