We have a boiler that supplies heat to three different levels. Each supplier has a pump and a thermostat. The upper level keeps giving a lot of trouble since we bought the house last year. There are times that when the heat is going on at all levels, the heat on the top level will not come up, the pump is trying to push it up but it wont come up.

The pump does NOT "push the heat up", it just moves it around. IF the water pressure is too low to lift the hot water to the upper level, then the pump cannot do anything. What is the pressure in the boiler?

You need to look at the PSI ( pounds per square inch ) of water intake
if the boiler does not have enough water in it then it will not rise with enough volume and pressure to create heat on the top floor. Another thing is air locks. There may be air pockets in the radiators preventing the water to flow evenly and that will prevent the heat form rising through the radiators. There are several reasons why this can happen.

I don't have access to that right now, because I am not home, but I will check later. As the pumps not pushing the heat up, it seems that whoever set up the pumps and the boiler, set it up this way, where the pump instead of moving the water into the boiler it drags out and the pumps sends it to the floor. I talked to a plumber before and he said that whoever set up this system did not know what they were doing.

The fact that the circulators are pumping away from the boiler, in itself, would not necessarily mean a mistake was made. It's a common practice.

quote; it drags out and the pumps sends it to the floor. I talked to a plumber before and he said that whoever set up this system did not know what they were doing.

That plumber should stick to plumbing, because he knows nothing about heating. That pump is EXACTLY where it is supposed to be. The pump does NOT "drag" or "push" the heat from the boiler, as I stated elsewhere. The water has to be high enough to reach the third floor and then the pump "moves" the heat through the system.

Actually, it is HOW they are supposed to be installed, so there is NOTHING "wrong" with it.

I can't say that, without knowing the particulars of the system. The plumber could be right.One of the postings sounds like Primary/Secondary. The primary should pump into the boiler.