Run Registry Editor (regedit).
Navigate to the following registry key:
KEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows Live\Messenge

For 64-bit (x64) OS, go to following registry branch instead:

HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\Windows Live\Messenger

In the right pane, right click on any blank space, select New on context menu, and then click on DWORD (32-bit) Value.
Name the new registry value entry as MultipleInstances.
Modify the MultipleInstances and set its value data as 1.
Start as many Windows Live Messenger windows as you want from Start Menu