Visio shapes can have multiple hyperlinks, but it can be a chore to add them with the Insert / Hyperlinks … command. Fortunately, Visio 2007 Professional has the Data / Link Data to Shapes … command.
If you were to have a data source, such as an Excel spreadsheet, that contains hyperlinks (see the example below)…
… then you can import these hyperlinks onto shapes, and they will be added, not only as Shape Data, but also as hyperlinks! In the example below, I have enhanced the Data Graphics to display the Shape Data on each shape.
When you save the Visio document to a web page as VML, then the multiple hyperlinks are available on each shape!
Unfortunately, the PDF and XPS exports don’t preserver the multiple hyperlinks – just the first one.