You should be able to. However, I am not up to speed on HDMI specifications so I don't know what resolutions HDMI 1.4 can support.
My primary rig has a Radeon HD 5850 which is connected to 2 monitors using DVI cables. My HTPC has a GeForce 9600GT it is connected to a monitor using one DVI port and to my HDTV using a DVI-to-HDMI adapter.
In general most graphic cards can support two monitors for the past several years; DVI / VGA or DVI / DVI initially. HDMI came into existance more recently so you may have a video card with DVI / DVI / HDMI, DVI / VGA / HDMI, DVI / HDMI or VGA / HDMI.
The video out signal is processed by the RAMDAC and it can only send out 2 video signals. Many video cards have 3 outputs, but that is more for flexiblity and convenience than the actual ability of the video card to output to more than 2 displays.
There are two ways a video card can output to more than 2 monitors:
1. Design the video card with another RAMDAC chip. These video cards are rare, and are somewhat expensive compared to a similar card with only one RAMDAC chip. For example, I believe I remember seeing a Radeon HD 36xx card that could output to 4 monitors, but it cost around $150 more than a typical Radeon HD 36xx card.
2. Get a video card with DisplayPort. DP requires it's own digital signal processor; I think it's called a TMDS module. This is why Radeons with EyeFinity can output to three monitors at the same time.
Nvidia does not have a single card capable of outputting to 3 monitors at the same time. In order to get NVIDIA Surround Vision you must use two GTX 500 cards in SLI to run three monitors at the same time.
Technically speaking, nVidia does have a single card that can output to three monitors at the sametime, the GTX 590. However, the GTX 590 is actually two downclocked GTX 580 GPU chips that are SLI'ed onto a single card.