KVM w/ Mutiple Monitors

Hello All - I'm not sure it's possible (and leaning towards no) but hoping someone can provide guidance. 

My current setup is a physical KVM I'm using between a personal desktop and a work laptop. I have a keyboard, mouse and multiple monitors. Two now but shortly adding a third. There are really no issues other than many cords and physical box to switch between. With getting a third monitor it would require a new physical KVM and I'm getting a new desk setup which won't be good for a bulky KVM switch. 

My goal is to use my desktop as primary and connect to the laptop. In testing with a trial license it seems that when I connect I can only take advantage of 1 monitor since it's a laptop.

My question: Is there anyway to take advantage of the real estate of all three monitors to act if three were connected to the laptop via Multiplicity?

I feel like I'm out of options other than a physical KVM to take advantage of a single keyboard mouse setup while using all three monitors. I can't use RDP either because of Windows Hello and requirements for device based certificates connected to TPM I'm unable to leverage RDP while accessing corporate resources remotely.

Thanks in advance.