It is possible to use three monitors in Debian; I've been doing this for a couple of years quite happily. My three monitors are all identical, and I have two identical video cards. I have done two (and perhaps three, I can't remember) monitors in the past that were not identical, though, and even with mis-matched video cards, and it has (usually) worked--although it's not always easy.
Your question doesn't tell me what type of video card(s) you have. You will almost certainly need two video cards, or maybe even three. You may be able to find a single video card with three (or more likely four) video ports, but they'll be expensive.
So the first thing you should do is make sure that your video cards have enough usable outputs--and note that just because it has (for example) an HDMI output and a VGA output does not necessarily mean that you can plug both an HDMI and VGA monitor into the card at the same time. Many lower end cards will have two physical ports, but only let you use one at a time.
It's also important to note that some video chip sets don't play well with others. Some years ago I was unable to do multi-head using an Intel chipset (I don't remember which one) with an nVidia chipset, because the Intel chipset's video BIOS refused to initiate when another video card was present in the system. (It may have been possible to work around this issue, but it was easier/cheaper to have my employer buy another video card).
To provide a more complete answer, you will need to provide additional information about your hardware. Which specific video cards are you using, and how do you have them connected to your monitors? If you could paste the output of 'lspci' that would be helpful.