Hi @thitt0927, sorry for the late response and welcome to the community.
The Arc is designed to connect directly to the TV with an HDMI-ARC port.
I would like to know more about how you want to set up the Sonos Arc, 3 Displays, and the HDMI switch.
Because we don’t recommend anything in-between the TV and Arc’s HDMI connection.
I’m also struggling with the same problem-
I frequently switch between my smart tv and projector. But now I got rid off my amp and surround speakers, when I want to watch anything on projector, I don’t get any sound as my Arc is connected to my TV. Is there any solution to this? Please help!
A device like the HDFury Arcana will take the HDMI input and pull out an eARC signal that you can send to the Arc. You can find more information here, as well as several other threads in the same area of the forum.