Some GPU cards you need to install an Active Adapter to get the third monitor to work. Here is a comment from a Overclocker.net concerning your R9 270 GPU card and using three monitors: R9 270 Refuses to Run More Than 2 Monitors...? - Overclock.net - An Overclocking Community
In order to use three monitors simultaneously, one of them needs to be hooked up via an active display port dongle. There isn't really a way around this, unless he's using one of the few new cards that happens to have the hardware support for three displays over DVI/HDMI. I believe the only cards that support this are in the R9 series.
I run 3 or 4 monitors from a pair of cards, but I hook up a max of 2 to each card. I need to disable crossfire in CCC to get the third and fourth monitors working. That or shell out for active DP adaptors.
E: Can't read the title :/ I'll look into the specifics of support for 3+ monitor support. What inputs are each of the monitors on, and what specific card is it?
E2: It appears to be only the R9 290 series cards that support 3 monitors from a single card without display port. The R9 270 is a rebadge of the 7870, which doesn't have the proper hardware to support it. There won't be a solution in software because the hardware simply isn't compatible. Your best option is to find an active DP adaptor, and plug it in. I've seen them for as low as $30 or so -- bought one for my dad's rig, and he's running a triple monitor setup off of a 5770 using it.