Is it possible to split a DMS-59 to three (individual non-mirrored) DVI monitors? I haven't found any such cables available for purchase on the Internet. If not through a cable, how would I accomplish this?
Considering that the DMS-59 only contains two sets of DVI pins I would not expect to be able to split it to three separate DVI connectors. At most I would expect to see a DMS to two DVI connector cables.
In the image below the purplish colour is DVI2, and the light green is DVI1, I cannot find a third DVI.
If you want three monitors out of a graphics card then you will need to buy a card that specifically states support for three monitors. Matrox have a series of devices that are specifically made for this such as their "TripleHead2Go" and I believe that high end ATi cards with Eyefinity can also drive three monitors as long as certain requirements are met. I believe as long as you get a card with three display outputs (with at least one "DisplayPort") then you should be able to use 3 or more monitors.
ATi have a "configurator" to choose a graphics card that supports more monitors.
Nvidia cannot apparently do similar on their older (pre-500 series) cards as without buying a second graphics card as this review and their own page for the GTX480 seems to suggest:
Nvidias 3D Vision Surround Requirements page only lists SLI systems as supporting more than two monitors.
If you only have a card with a DMS-59 output then you will only be able to split the output to two DVI connectors using a cable such as this one which looks a little like this
Without fitting another graphics card into your computer or getting a card that supports more displays there is no way you will be able to drive more than two monitors.