I was wondering if there is a way of getting around the exception that is
thrown by most parsers if the document function is called for a file that
does not exist.  I would just like to continue on in the processing.

There is no standardized way to do this. The spec says, the
processo may either throw a fatal error, or continue using
the empty node set as result.

Check the documentation for your processor whether there
are command line switches or an attribute of the transformer
object which controls the behaviour. Saxon for example
recovers by default, but these non-fatal errors can be
set to be fatal.

If you are using a Java based processor supporting JAXP,
you can write your own URIResolver which checks for the
file and supplies a dummy XML if it doesn't exist.