Adjusting temperatures in a multi-family building

JWoodoff

This is more a theoretical than a practical question. I live in a 4-story 8 family building dating to 1909 with one-pipe steam heat. The boiler is fairly new. The thermostat is in the public hall on the second floor. There is a radiator in that hall on the first floor. The third floor apartments are warmest, followed by the fourth floor, then the second, and the first floor are coldest. The first floor is over a cellar, unheated except for the insulated steam mains. Some of the 3rd and 4th floor radiators have thermostatic valves or adjustable air vents that to some extent moderate the uneveness in temperatures.

My theoretical question is, if the radiators on the 3rd and 4th floors were all shut off, or severely limited in order to completely even out the temperatures throughout the building, how would that affect the operation of the system? Would any energy be saved? Shutting off the steam to the upper floors wouldn't cause the radiators on the lower floors to be any hotter or warm up any faster, so wouldn't the boiler have to run the same amount to bring those floors to the specified temperature? In that case, would the boiler be effectively oversized? What happens to the excess steam that is no longer reaching the upper floor radiators? In other words, in this system, is any energy saved by lowering the temperatures on the upper floors?

question

Theoretically if you shut off the radiators to the top two floors you are only heating the bottom two. You would save energy. The occupants on those two floors would not be happy.
There may be riser pipes going to the ceiling of the top floor that would still be giving some heat to them. It seems that you have some venting issues on the first two floors which should be addressed . I would try using heat timer vari vents on the lower floors. They are the fastest venting air vents that I'm aware of.
There are articles about balancing the steam that you may want to look into. Good luck!

SteamingatMohawk

Before you go spend any money on Heat Timers or any other vent valve for that matter, I beg you to take a look at this report

https://heatinghelp.com/systems-help-center/category/steam#air-venting

You don't have to go through the details of balancing to get an idea of the capacities of the different brands of vent valves to help you choose the best one(s) for your needs.