Common methods for doing this recomend you use the “sudo” command to run Skype as the root (administrator) account - don’t do that, it’s a very bad idea for security. Skype doesn’t offer a built-in way to do this on Mac OS X as it does on Windows. You can keep double-clicking this shortcut to open additional instances of Skype.
Give the shortcut a name like “Skype (Second Account)”. 'C:\Program Files (x86)\Skype\Phone\Skype.exe' /secondary
For example, on a 64-bit version of Windows, it should look like:
In the Target box, add /secondary to the end. Go to your desktop, right-click the Skype shortcut you created, and select Properties.