Changing steam radiator configuation

hk

I am an architect but do not know if my posible solution will work for this situation:

I live in a 20 floor building from the thirties that is heated by cast iron steam radiators (two pipe system). I am trying to combine small studio two units vertically into one unit with two bedrooms on the lower floor. I need to provide heating (building code issue) for these bedrooms but the new floor layout will create a bedroom that is 10 -15 feet away from the existing steam radiator and piping. I would like to pipe over to the new bedroom with pipes hung from the underside of the concrete slab. Would the pipes need to be sloped? Can the steam pipe travel almost horizontally and then drop down a wall to the radiator? If this is not possible, does anyone have a solution to this problem?

Thanks in advance for your input.

hk