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
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.
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:
Before Connecting Mutiple Monitors or a Monitor and a Television to
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.