Another way would probably be to have one of both universes be fiction inside the other..and then something happens. For example: There is nothing to say that at least the old Dr. Who series did not exist in Trek universe (the new show would not have existed since its creation would fall right into WWIII if I´m not mistaken). Since Paris is already fascinated with old scifi shows he could come across Dr. Who and make a holo novel. "Something" happens to make that holonovel "real". Of course you would have to find a new and innovative way to do that....something other then the usual "trapped on the holodeck". Maybe thery finally find a way to convert holomatter into regular matter. An experiment with the conversion technology goes out of control and converts the entire running holodeck programm.