Adding a filter to an established tank does absolutely nothing to change the amount of bacteria in a tank. That is only accomplished by increasing the ammonia production in the tank. All that adding another filter will do is spread out where the bacteria lives.
Because the bacteria is basically immobile inside the biofilm it uses to attach to hard surfaces, only a small amount of the bacteria are motile. How much depends on the levels of nitrogen present in the water. When it goes down, the bacteria can sense this and more of them become mobile so they can move to a place which has what they need. When they have that where they are, the numbers that are motile will decline.
Because the bacteria are relatively immobile, where they will have the greatest concentration of numbers is where the things they need are regularly available. What they need is basically oxygen, ammonia/nitrite an inorganic carbon (carbonates/bicarbonates.CO2). There are other things they needs as well such in smaller amounts. All of this must be delivered to them inside the biofilm.
So, adding a filter doesn't increase the number of bacteria. What will happen over time is that some of minimal bacteria that is mobile will land in the new filters. They will start to multiply there. At the same time they will slow or cease multiplying elsewhere. So in a matter of weeks what will happen is the total amount of bacteria in the tank will not change, it will, in effect, move to other locations.
The bacteria doesn't do this by actually packing up and moving elsewhere. It happens by where the bacteria multiplies and where it does not.
At the center of the entire cycle is ammonia. The level of ammonia determines both which strains of bacteria will colonize and in what sort of numbers. The more ammonia that gets processed into nitrite, the more nitrite oxidizing bacteria will colonize. Finally, if conditions are right, there will also be denitrifying bacteria colonizing as well. However, these need an anaerobic environment so are harder to have establish in many tanks.
This boils down to a supply and demand type situation. The ammonia is the supply and the bacteria are the demand. When there is excess food, the bacteria multiply. When food is in short supply they do not. This means the size of the bacterial colony in a tank will always size to the available levels of ammonia.
Think of this in terms of a fishless cycle. Set up three tanks of equal size, contents and filtration. In one add ammonia to produce 1 ppm, in another make that 2 ppm and in the third make it 3. You will see two results. First, the tank with 1 ppm will be cycled the soonest and the one at 3 ppm will take the most time to become cycled. This also means there are more bacteria in the tanks cycled using 2 ppm than using 1 and that the tank getting 3 ppm will have the most bacteria and will be able to handle the biggest fish load.
The number of filters on each tank will do nothing to change how much bacteria colonizes in each tank, the amount of ammonia available is the determining factor.