What size and brand is the power supply? Looks like you have at least 1 PCIe x16 slot. What's your budget?
From an amazon.com review:
"UPDATE #2: I have successfully replaced the GT 630 with a GTX 650 Ti SSC (SuperSuperClocked). I have seen a lot of people on here and the web complain that this computer cannot accept any video cards except the OEM, FALSE! Here's the secret to make it work. BEFORE taking out the GT 630 boot into the BIOS by pushing DEL when the Acer boot screen comes up before Windows 8 launches. You now need to look for something called "Secure Boot" and "Disable" that function. Now look for an option called "CSM" and enable that option and it should say legacy now. Now you can shut down the computer and install the GTX card. The first time you boot up the computer it may restart at the boot screen, but on the second boot it should boot fine. At first your resolution may look incorrect but this should auto-correct in a few seconds if you are using another nVidia 600 series graphics card. If you are using another series or brand, you are probably going to have to update the drivers. Upgrading to this card increased my WEI ratings for video from 6.7 to 7.4 (I might re-run the test now that the computer has been booted a few times). First thing, I tried Saints Row 3 on Ultra settings and 1600x900 resolution (should be adequate for 24" monitor), it looks beautiful and runs smooth! One last consideration when upgrading the video card, MEASURE the space you have to work. Some of the ATI cards give more bang for the buck but they are generally larger. They might still fit, but I decided to play it safe by getting the best of the 650's (Plus I'm NOT rich)... which is still a considerable improvement over the factory card."
Edited by IchibahnSLC - 4/3/13 at 10:56pm