Dual Monitors with DisplayPort and DVI-D

The DisplayPort Spec supports the daisy chaining of multiple monitors, but not the splitting of the signal. Unfortunate, to support this you need to have at least 2 DisplayPort equipped monitors that support daisy chaining (of which there are none to my knowledge).

Given your situation, your best bet would be something like the Matrox TripleHead ToGo, which allows you to connect multiple monitors to a single port (and tricks your computer into only seeing one while spreading the image across several).

Using a solution like that, your main limitation is the power of your graphics card and how many pixels it can render well.

It should work with an HDMI -> DVI-D (DIGITAL) adapter, but have a look at this from the Intel website:

What are the system requirements for Multiple Display support? Your computer must have the following:

Physical video output connector(s)

Your computer must have a video output connector or connectors to which one or more external displays would be connected to. Some laptops may have additional video output connectors on a docking station, port replicator, or via the laptop manufacturer’s special video cable. On desktop systems, some computer manufacturers may offer at an extra cost an add-in card (referred to as ADD2) which adds video output connector to the computer.

Two or more display devices are connected.

Display devices may include an analog monitor, notebook’s built-in display, external monitor or flat panel display with analog, DVI-D, DVI-I, HDMI*, or DisplayPort* connectors, or television with S-Video, Composite, Component, or D connectors. Not all display device combinations may be supported by your computer. Please check with your computer manufacturer for information on the supported multiple display configurations for your computer.

An Intel® graphics driver is installed.

The Intel graphics driver’s Properties control panel allows you to set a multiple display configuration. Not all multiple display configurations may be supported by your operating system or by your computer. Some examples include: The Starter Editions of Windows Vista* & Windows 7* do not support Extended Desktop mode; Many computer manufacturers disable the Twin mode. Please check with your computer manufacturer for information on available and supported multiple display configurations for your computer.

http://www.intel.com/support/graphics/sb/cs-031040.htm

***UPDATE:

I might be wrong. Look at this, and check all the comments. It appears people have mixed results. I've seen multiple outputs work on many Optiplex models so it might still be possible to do it if you have the right drivers:

http://en.community.dell.com/support-forums/desktop/f/3515/t/19410045.aspx

Before Connecting Mutiple Monitors or a Monitor and a Television to Your Computer

To support dual monitors or a monitor and a television, you must have an optional graphics card. If you are connecting more than one monitor, ensure that the connectors on your monitors (whether VGA or DVI) match the available connectors on your computer, or that you have any necessary adapters. For example, if you have a VGA monitor that needs to be connected to a DVI port on your graphics card, you must have the optional DVI adapter.