You can create and reference a common configSource for the configuration section(s) involved. For instance, if you wanted a common set of AppSettings, copy your current appSettings to a new file (say appSettings.shared.config) and replace them in both app configs with this:
<appSettings configSource="appSettings.shared.config"/>
Here's more documentation: http://sunali.com/2008/01/23/configsource-property-dividing-configuration-files-into-pieces/
Far as I know, this cannot be done for an entire file, only sections, and each section will need its own file (and the section must still be declared in the configurationsections element of the app.config). But, this has a number of really cool uses; for instance, you can separate your connection strings into files geared towards different environments (local, development, testing, staging, production) and by changing one filename in one place you've now pointed your app at the different environment.