Multiple Monitors on the client, 1 or none on the remote

Here’s the problem I’m trying to solve:

I use my computer system for multiple things to include as the computer side of a ham radio software defined radio. It’s a flex radio 6300 running smart SDR. Smart SDR uses virtual ports to control audio both receiving and sending. To get the system working to do digital contacts requires making sure that the sound set up on the computer is pointing to the flexradio software.

The problem I’m having is anytime I use my computer for anything else such as listening to a YouTube video or using Dragon NaturallySpeaking to write a letter, it tends to break the functionality of the smart SDR software.

Additionally, I run 4 monitors.  That allows me to have my logging program on one monitor, smart SDR on another, and the software that makes digital contacts on a third, while leaving the fourth to run searches on the Internet.

I’m beginning to think that the best way to solve this problem is to buy a dedicated computer for the flex 6300 radio. Problem is how do I switch two computers between four monitors.  I don’t want to have to run 8 monitors.

I already use team viewer to access my system remotely, to include running the radio.

To the meat of the question. Is it possible to have a simple small computer connected to my ham radio equipment, then use team viewer to access that computer via my main computer, and configure team viewer to display multiple monitor instances on the radio computer, even though in reality it will probably have only one if not zero actual monitors attached to it.

Does anyone know if this is possible with team viewer? Any input would be appreciated thank you.