What do you exactly mean by launching multiple dialogs?
User clicks a button once and sees say 3 dialogs?
The JOptionPane.showXXXDialog creates modal dialogs. So that won't work for the above scenario.
Only way for you to create and display non modal dialog windows yourself, using say, JDialog or JFrame.
By the way why do you want to launch multiple dialogs? It is very bad usability.
Combining the contents of the various dialogs and displaying them in a user friendly manner, in one dialog would be good design.