Question Three monitors with a KVM switch

Jun 28, 2020
first time posting. I'm trying to use three monitors in extended view between two machines using a kvm switch. I want to find how to do this with the least amount of hardware and preferably using hdmi with each monitor. I bought a kvm switch that can toggle 4 pc but has only one output (hdmi). I then bought a 4-port hdmi splitter and connected that to the output of the kvm; this resulted in only mirroring one display three times (to each of my three monitors). I'm lost on why this didn't work and what hardware to buy for a solution. I can use all three monitors just fine with each machine individually but I want them both connected to a kvm of whatever kind so I can just hit a button to switch between work machine and home pc.

machines 1: laptop lenovo thinkpad t460s

machines2: custom desktop with nvidia geforce gtx 1660 ti

the three monitors are all Dell P2419H

Thank you for any help you can provide!