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This has come up from time to time, and I think some of the Caleffi articles address it.

Basically, you are on the right track. The existing boilers are in the basement? Then you would them up as zones coming off the single boiler. I would drop the old air tanks on the roof and use a conventional -- and single -- expansion tank on the system. You will have to pump the system, and it should be set up primary/secondary. There are arguments in favour of a single secondary pump and zone valve, and there are arguments in favour of zone pumps instead. Chevrolet vs. Ford. Since each zone is its own floor, you won't have anywhere near the balancing hassles which usually happen when going from your type of system to a pumped system -- which is one good thing! Further, since your air tanks are on the roof already, the pressures in the system will be similar to what has been there, so leakage shouldn't be too much of a problem, if any.

More details?

Boilers on each floor? Odd setup, but then -- something new every day. Still, since the air tanks were on the roof that won't change the pressures, which is a good thing.

You should be able to pipe that with a feed and return for each floor from a manifold in the basement, fed by the mod/con. As I note, either zone valves or zone pumps. Oddly enough, once you get the system filled and purged, the extra height to the third floor, for instance, won't make any difference.

I would use fairly generously sized risers and returns, and I certainly would go primary/secondary.

Is there a boiler physically on each floor or a boiler in the basement for each floor?

To be a gravity system it seems they would have to be lower than the radiation.