Yes A cross over but I have always been more intrique with the idea of introducing the elements of one into the universe of the other for example i was thinking of writing a story and this came to mind.
In 2381 a Starfleet vessel finds a disabled Republican crusier (the one seen at the start of Phantom meneance) aboard the away team find 100 or more near death from lack of life support. Once aboard the Starfleet ship all begin to recover quickly with little medical attention. They explian that they were being pursued by Imperials when they encountered a Time/Space anomoly the ship was violently tossed about and had suffered damage and they had been adrift for close to a week. As the investigation continues it is soon realized that these people dressed in their brown robes are very peacable but still very strange.
Meanwhile these Jedi discuss among themselves they detect the force as being present but yet no one amoung these people sense it. That their Histories have much to be admired and they all are impressed by the Code of the Prime Directive which they see as a means which has prevented this universe from degenerating into the same type of one which they have just left. They all quickly conclude there is no way for them to return to their universe and that this is were they will live from now on.
Their leader Din Ja Quon, asks to talk to the Federation councle on an important manner. Starfleet still unsure has reservation and even though PSI detection is off the scale with these people there seems to be little to be worried about. The meeting is approved and the Jedi ask to form a new Jedi councle to serve the Federation after a sufficent demonstrations of all their powers both PSI and normal ones such as Diplomatic and militarily.
Questions:
Would the Federation accept such an offer which would replace Starfleet in someways?
Would the Federation even be so open as to allow these Jedi to exist openly among the Federation?
Would the Jedi allow the Federation to understand and use the technology of the Republic (Hyperdrives, Light Sabers etc..)?
How would the other powers in the Trek Universe react?
Would the DarkSide eventually appear, and from where?