That should be possible. I good idea would be if Advanced - Open New Instance of UltraEdit would open a new instance and when SHIFT is hold while executing the command, the current file is opened in the new instance. You can send a feature request email to IDM.
A workaround could be following:
Configure a user tool with Menu Item Name Open File in New Instance, the Command Line C:\Program Files\IDM Computer Solutions\UltraEdit\uedit32.exe /fni "%f", an empty Working Directory and on the Options tab Windows Program selected. Next make sure that all other check box options on the Options and Output tab are not enabled and the radio options on the 2 tabs have their default values, especially Capture Output should not be enabled (by default checked).
Then customize the popup menu and add the command for the user tool.
Best regards from Austria