If you're using 4x external monitors that could be a lot of pixels to move. What kind of video card is in your computer/laptop? You might want
something like this which is powered and has 4x HDMI/DP outputs. The only down-side is you may be capped at a 60Hz refresh rate at anything over 1080p per screen.
I ran a similar KVM/dock and was stuck at 60Hz with a high-refresh rate monitor. It was not fun. I decided to ditch multiple monitors and go with a single 34" monitor - so consider 2x 3440x1440 monitors instead of 4x 1920x1080 monitors.