To give the best answer, I'd need to know more about your environment.
If you'll answer these questions, I may be able to suggest something.

1) What is the database behind the web service?  (Is it another Access
database, is it SQL Server, or is it something else?)
2) Is changing the code in the web service an option?
3) Is someone on the project able to write managed code (C#, for
example)?
4) What is the business reason behind your request?  Specifically, why
are you storing data in the Access database as well as in the database
behind the web service?
5) You have two issues: retrieving the data and storing it.  We may be
able to store the data in more than one database, but of course you can
only retrieve from one of them (you can't fit two data items in one
field!).  Which database will be the authoritative source?