Is the Dell XPS able to handle a Geforce gtx660 graphics card? Will it be okay on the motherboard and the PSU? If not what is the highest that I could upgrade my graphics card.

The board can, but the chassis has limited cooling  and you might be better off moving it into something with better ventilation.

I have an XPS 8700 (Mid 2013). Mine came with an NVIDIA GT 635 Graphics cars with 1MB DDR3 Memory. I swapped it out for an NVIDIA GTX 750Ti Card with 2GB DDR5 Memory. I also did a DELL update to the BIOS from version A05 to version A08, via DELL's website (Just a precaution I took). Now here's the thing.....The new card occupies a double slot rather than a single slot like my old one and very important was the power requirements for the card called for 400W power supply. My XPS 8700 had 460W, therefore I felt I was really pushing it and the computer may cut off and on from power consumption to other devices, so I upgraded the power supply to an ASUS 650W Gold supply. The nice thing is it is a great power supply and is completely modular (you only plug in what you need!). My system is humming along just fine now, and with 12GB of memory it's virtually on cyber-steroids! You can definitely upgrade your card, with a little work. Hope this helps! Feel free to contact me for any other questions.

MadMaxx2004 

Congratulations on a nice upgrade.

Bev.