Is it at all possible to use multiple displays with only a built in VGA output and no DVI output available?
When adding an extra video card, it might or it might not depending on your system's configuration. A more elegant and better solution would be using an extra video card that has multiple outputs.
Without adding an extra card, splitting the signal might be possible, but this would not add an "extra" display, merely a duplicate.
What a splitter would look like:
DVI in fact, might not even work AT ALL since it has restrictions.