Vostro 3268 adding second GPU

Problem is you have only one slot available for a video card. You cannot use both the integrated Intel video that comes standard on your model and a card since it is either/or not both. If you add a card you would need one with dual monitor support but it won't support 3. If you have a discrete card now it can already support 2 monitors. The card you would need if you have integrated video now is this one that could have been ordered when you chose the options to configure your purchase-

NVIDIA GT 710 LP(Low Profile) with 2 GB memory DDR3  --but still only for 2 monitors.

Wow, I wasn't aware of this. It seems a bit strange that it's either/or situation, such a let-down.

Take a look in this video: https://www.youtube.com/watch?v=dUl0sJ-SK8s

Is this possible on my Vostro? DVI and HDMI on one slot and VGA on the other (I think there are two slots available on the back). Will it, then, support a 3-monitor setup?

Most PC models disable onboard video when there's an add-in video card. Others may not, as long as there's at least one monitor already connected to the add-in video card. So worth trying to connect a monitor to an onboard port with one monitor connected to your add-in video card.

Many modern add-in video cards support 2 monitors; some even support 3, so check the specs. If onboard video is disabled and your card only supports 2 monitors, you could get a USB>{video} dongle where {video} is a port supported by the 3rd monitor.

Better to choose a USB3>{video} dongle because you'll get better performance than with a USB2 dongle, but at somewhat higher cost. And make sure whichever dongle you get supports the version of Windows that's running and the optimum (= "native") resolution setting recommended for the monitor that will be used with the dongle.

So, I installed a Gigabyte Radeon R5 230, I enabled Intel Multi-Display in the BIOS and now I can use both the onboard graphics card and the add-in card simultaneously. Currently, I connected 4 monitors and everything's working great.