Look on the bright side, at least the GTX660 isn't a total waste of time unlike a lot of stuff people have tried to use to avoid an upgrade. A GTX960 will be more than adequate if you feel the need to comfortably upgrade the GPU (not tested personally at 4K, but it's apparently not bad at 4K - better than would be expected, but 1080 is more than adequate really). If your MB will support it, go with a mid-high range quad-core if you're not already using a quad-core CPU, and maybe do that first and sort out a GPU if needed.
Running an FX-8350/GTX 960 (ASUS factory o/c card) myself which i use at 1080i type res/depth via VGA still (got better uses for HDMI sockets than PC's). Once you get within sniffing distance of meeting the recommended specs of the game (or near enough), it's just a matter of figuring out the weak link. In my old HexCore system, it was the Nvidia 315 card and sadly the cost of a new MB to support my personal memory requirements needs (32Gb) and a suitably uprated GPU put matters into new system money.
It's not entirely perfect, like with Ian, i get the odd random drop - but it's more frequent when i'm running mods and on external camera in a very detailed scene.