If your main drain pipe (sewer stack) from the upper floors of your house comes down through the basement and through your floor, you probably have a relatively easy job. I DO recommend you get two or three pro plumbing contractors to quote on the job.
We did what you ask about - and had a contractor do the work. The new bathroom (toilet, sink, and corner shower) was located close to the main sewer stack pipe. The contractor simply used a small jackhammer (might get away with a sledgehammer?) to break up the concrete floor in the spots needed for the job, dug out some dirt under there, then tied into the existing main sewer line running under the floor and starting from the main stack vertical pipe. Concrete floors often are NOT super-thick and tough - after all, they only have to support modest floor loadings and are fully supported from underneath by soil. The contractor ran new sewer piping for the three fixtures below floor level in trenches in the ground, thus creating the roughed-in fittings for the three devices. Then he filled and tamped the soil around the new pipes and poured new concrete over that to fill in where he had pounded out the old. The concrete needs to be smooth, of course, but it ends up covered with new flooring so it does not need to look fantastic. Then the rest of the job was typical stud framing, sheetrock, etc., and finally installing the three plumbing fixtures. Running water supply lines to each was easy - just tap into existing lines and drop down to the right locations, through new walls, and connect.