There are a couple of ways of doing this, though as others have mentioned, the biggest issue is the VGA monitors.
As @chemmajorp53 says, the "proper" way to do it is with an MST hub on an AMD card. Here's a four way DP++ hub, which would allow you to use 4 DP to VGA adapters:
http://www.club-3d.com/index.php/products/reader.en/product/multi-stream-transport-mst-hub.1655.html
But you're talking several hundred US dollars for the adapter and cables.
I've had very good success in the past running multiple graphics cards on Win7 and later. Assuming you're talking about just desktop use, and not gaming (which is a totally, totally different story), you should be able to use multiple cheaper cards, or a card and your integrated GPU, and it'll all work pretty seamlessly.
Do you have integrated graphics? How many display outputs (and of what type) can you get from that?
Do you have a graphics card already? How many display outputs (and of what type) can you get from that?
Can you post your motherboard and CPU so we can see what's possible?
Are those 4 VGA monitors really VGA only? They don't even have DVI inputs? That would help!