Unfortunately we have very little information about which multi-channel sound devices work with Audacity. There is a little information in this topic: https://forum.audacityteam.org/t/multi-channel-recording-in-audacity/15644/1 You may be able to get additional information by searching Google.
When you eventually get a 4 channel device, please let us know how well it works with Audacity - this is one area where we totally depend on user feedback (unless some kind and wealthy soul donates a load of hardware 
)
Reviews of audio hardware with Audacity are extremely welcome in this section of the forum: http://forum.audacityteam.org/viewforum.php?f=27