ok when making suggestions lets not forget the timeline of KOTOR, its some 3900 yrs BBY (before the battle of yavin) that would make many connections that have been suggested (for example the sith antagonist eventually passing his knowledge down to palpatine) erroneous, nice wishful thinking but in reality would probably only be in holochron or ghost form...
i like a lot of the suggestions i am reading, and i think one of the best was drawing from the original trilogy for a rough formula of what KOTOR3's purpose and direction would be (ie resolution, finality, victory, answering of questions, and tying up loose ends)
heres some ideas i have in my head to add to a lot fo the posts here
the players main character would not be the exile at all, instead they would be retracing the steps of the exile through a vast array of planets in the outer rim...
heres how:
a republic patrol encounters the Ebon Hawk floating lifelessly in a yet undisclosed location, the ship is for the most part intact, but it has suffered from elecromagnetic damage and the crew is missing (the exile had to abandon ship to continue their search for revan) due to the damages, the last record in the navcomputer is somewhat disjointed, but many of the places that were visited prior to the ship taking damage have been retrieved from the memory banks during a refitting of the craft, and this is where our main character draws from to locate the two missing heroes of the republic. since the sequence of the waypoints was not recovered, he/she must by trial and error go to each one of the planets that were recovered from the navcomputer and search for clues on each respective planet (in no particular order) once enough of these clues are assembled they will finally lead to both the exile and revan who have decided to collaborate and find the object of their pursuit...
why strictly the outer rim? the logic of this is due to the time spread between KOTOR1 &2 and Episodes 1 thru 6 the galaxy was still much unexplored during circa 3900 BBY, and by the time we get to Episode one many of the planets known to the current republic were not charted 3000 years before. it would also ease the decision making process in finding suitable worlds to explore and what names they would have.
those outer rim worlds would be inhabited by many species who were influenced heavily by the infinite empire during its time, so the language would be similar to a corrupted rakatta or other of the three Builder species and the original sith language. The exposure to the republic would have been limited to jedi encounters (not unheard of) and may make some of the translations easier with the aid of a new model protocol droid or a hand translator(?). Zoist would be an interesting planet to make one of the focal points of the galactic exploration and attempt to trace the exile and revan...
the point of the planet hopping would eventually be revealed as the discovery of a superweapon that would be the only way to defeat the true sith once and for all, and the possibility that the main characther finally meet both revan, and the exile in the last few quests prior to the climactic battle with pleadings and insructions from them on their findings and how they would aid the galaxy in warding off the invading true sith...
there may also be several colonies where basic is spoken on primitive worlds say during a crash landing and it would ease the language barrier a bit, especially if there were another world that the exiled mandalorians had set up camp on, so the quest there would serve the purpose of rallying the mandalorians to the greater cause of the galaxy
all this hopping would be pointless unless from time to time the main character would have to rendevous with the people who sent him/her, so there would be various times that they would cross paths as the main character zig-zags through the outer rim. (it would also be a good way of gathering all the mandalorian exiles at one pont where the leader of one of the fragments is known to have the previously agreed upon locations of the other clans and once they make contact with the republic they would take over from the main character and find the rest of the remnant and furnish them with means off their respective planets. once that is completed they will collaborate with the republic and begin to rebuild their forces to unprecedented levels. the republic would also employ them as military advisors, and the scematics for mandalorian war machines would be handed down for the republic to construct with the oversight of the mandalorian generals)
then with the pressure building more and more each time, the encounters with true sith would be more and more frequent during these rendevous. and the combined strength of the mandalorian/republic fleet would be more and more evident with each rendevous. during several of these encounters especially those further away from the core, small sith scout patrols would cross paths with the republic/mandalorian fleet and a small battle would ensue, each time though it would become more and more of a challenge indicating that they were closer to the true sith invaders...(with the availability of better game engines since KOTOR 2 this would make even more realistic space combat a good idea. so instead of looking out a turret to shoot down sith fighters, one would have to fly the craft and shoot their way out of the battle to a designated waypoint where they would finally make the jump to light speed, or to the safety of a capital ship, or even one of the local planets)
the climactic battle would be great if the republic and the mandalorians did team up to go up against the invading true sith fleet, i would love to see the basilisk war droids introduced into a combat scene, and even the cutscenes prior to the battle, just think of the massive battle that woud ensue, it would even make the battles of the prequals pale in comparison...
anyway the final battle would also involve much more than just watching the cutscenes of what happens, it would actually be playable!!! not only would you be assigned to a flight of ships on the offensive, but there would be regular updates to the many battle objectives assigned once each one is completed until the final assignment was disseminated and the superweapon was activated
unfortunately the only way i can see that going would be to use the combined forces of the republic and the mandalorians to draw the sith into the kill zone and annhiailate all the fleets involved, leaving huge disbled floating chunks of space junk
and of course the final mission of the players team would be to escape the battle and retreat to Republic space to bring the news back to the homefront that they had just averted the greatest disaster to the galaxy