Is it possible to upgrade the graphics card on my Sony Vaio Fit 15 SVF15A1S2ES? Currently it has a Nvidia Geforce 735M which isn't quite good for next gen games.. if its possible how much would it cost approximately to upgrade?
No you can't, very, very few laptops have upgradeable graphics cards, on all lower end laptops like yours, the GPU is soldered to the mainboard and cannot be removed. If you need more graphical performance, while remaining mobile, then you have to buy a new laptop, and have a considerably larger budget. Laptops with GPUs good for next gen games will be quite pricey because you pretty much have to go for something close to top of the line in order to match the specs of the new consoles.
If you really want to play next gen games without buying a next gen console, and don't have $1500+ to spend, I would recommend looking into building a desktop system, you can get a lot more power for a much more reasonable price.