This is a pretty big job. I don't understand when you say you have no vents for the second floor bathroom? If this is so, it is a big problem.
And if you do have a vent stack running up through to the roof, you cannot use this as the drain to connect the 3rd floor bath to.
As with many old buildings, it sounds like your plumbing may have been cobbled together over the years. Now is the time to possibly make it all right, rather than compound previous errors and get to a point where nothing works at all!