It will be very small screens if you were to to reduce size of each so you have 4x4 grid (if I understand correctly what you want). And yes, smart enough KVMs would do that (allow you to multiplex several input channels to one output, similar how set top boxes can do for TV signals. You can ignore their "keyboard/mouse" parts of the KVM, of course).
Note however that it would probably cost much more than 16 monitors...
I'm not sure it's allowed to send links to commercial company products, so I'd just recommend to search for "split vga multiplex" or similar phrases.
Mostly you'll find then in 4 channel variants, so you'll need 5 of them (4 to multiplex 4 PCs each, and fifth to multiplex 4 multiplexers).
What you describe is not possible. What is possible is using a Remote Desktop client with a single machine even tools to exactly that do some more research on the subject – Ramhound – 2014-10-24T22:50:14.183
A mention of OSes would be critical in answering. You'd also want to talk about how the pcs are linked, and what you're actually trying to do. – Journeyman Geek – 2014-10-24T23:49:41.280
It sounds like you are looking more for a broadcast switcher $$$ , especially it being a broadcast company. with one (or2) of those you could view smaller , and even select to pip or full a particular one. Check out the pro video sales location, they would be happy to tell you what they have. There are consumerish versions of such things for security, sold (again) by the same people. – Psycogeek – 2014-10-25T02:47:23.890