There is a solution to your problem.
To run more than 2 monitors in eyefinity you need either a native displayport monitor or active displayport adapter. In your case you will be using DVI ports to you will need an active displayport adapter.
Here is one - http://www.newegg.com/Product/Product.aspx?Item=N82E16814999030
Get the adapter.
Then hook up your monitors, 1 via dvi, 1 via dvi, 1 via active displayport to dvi.(By the way hook all of them up to the same video card.
Also if your video card has mini-displayports instead of displayport, choose this adapterhttp://www.newegg.com/Product/Product.aspx?Item=N82E16814999034