The economics of operating a flying school are such that most accountants would advise you to invest your money elswhere where it might show a profit.
The number of clubs/schools on an airport depend very much on who owns the airfield. If you own the airfield, a maintenance organisation, a flying school and possibly a restaurant you can probably make a reasonable return on your investment so long as you don't allow other schools to trade there as well.
Where lots of schools trade from the same aerodrome there is usually insufficient bussines for them all, but the owner makes his money from rent fuel and landing fees. Maybe aircraft rental as well.
The big airfields don't like light aircraft, because they bring in complaints, not money; so they raise the handling charges to the point where they cannot afford to operate.
There is a saying in aviation, how do you make a small fortune? You start with a large fortune!