I agree with Brian. In addition to extra work, expense, and materials, you reduce your useable space. That is fine if you began with 9' rooms (height) but if you started with 8' rooms, you might wind up with about 6 1/2' of useable space. You can see the problem.
Perhaps a better solution is one I recently saw in a timber frame house I was visiting. The plumbing was run across the ceiling of the first floor up aginst a beam and a chase with a mitered corner was built to but up aginast the beam on the bottom so it was the same level and was hinged with European hinges about every 3' and on the side was held in place with snap locks so it could be lowered for repair/inspection/service& cleanout.The same was done with the stacks along the wall. To make it match, a false chase was created on the opposite side of the room. It was very neat and required only a minimum of extra material and labor and kept the upstairs the same as it was. Since the beams were 6"x6", it posed no problems at the intersection where the sweep tee received the line coming across the ceiling. It looked very clean, professional, and gave the appearance that some forethought had gone into the engineering so as to widen the beam at this point to carry additional weight loads and no one even paid attention to it. Had I not been looking to see how the plumbing was handled, I would not have seen it. The water supplies were included in this same chase. Perhaps this is a cost reducing idea you could adapt for your use?

Keith in Houston