A quick shot at Google using "multi-monitor kvm" search found a company with the features you've noted. Good thing your budget is flexible.

Dual monitor systems appear to be much more economical than triple (in progress, per one site) or quad.

[KVM Switches Online][1] does a great job of categorizing the products available, specifically in this case, allowing you to pick HDMI for dual or quad monitors. [One of the switches][2] supports USB 3.0 while the other list as USB 2.0 only. The USB 3.0 unit is listed as a hub, but the image of the front shows 3 ports. The rear of the unit has 2 USB ports marked for keyboard and mouse.

[![KVM front image][3]][3]

[![back of kvm][4]][4]


  [1]: http://www.kvm-switches-online.com/dual-monitor-hdmi-kvm.html
  [2]: http://www.kvm-switches-online.com/sv340h.html
  [3]: https://i.sstatic.net/NGMjv.jpg
  [4]: https://i.sstatic.net/t9JtO.jpg