Create a suitelet for the user to be able to select invoices to print (maybe user selects a saved search or marks invoices to be printed). This could then launch a scheduled script or map/reduce that saves all the files in the filecabinet. Then it's a matter of downloading the PDFs.
Ooor
Fix it so that the standard(advanced pdf) print function works as you want and then use the standard way of printing multiple invoices