One sadly simple way of making a profit which a (state) school I was involved with did, is lease the building to a private company as part of their buildings portfolio allowing them to value their company higher for shareholders, and the school then rented it back paying more each time it was supposedly 'upgraded'.
The company's then responsible for maintaining it and can apply for public money for building contacts especially as the school was due agreed money because it was in such poor state.
End result was existing buildings falling to pieces, portacabin classrooms to cope with unuseable rooms, and new sports buildings going up on the cheap and rented out, new very fancy incredibly expensive disabled access built with different grant money, but created non wheelchair accessible, but caused schools rent increase, but wheelchair lift can't be fixed because no grant available, most of the buildings left disabled inaccessible as all grant money exhausted on non functioning entrance, but box ticked for disabled accessible. (not if your a child in a wheelchair, but in theory you can go) School now can't get more grants for years because it's had it's lot.
The company had nothing to do with the education of the kids, but poor management used the situation as an excuse for many things including not enough books for even one per two students.
They are now out of the rental contract but the debts left mean the teachers are being expected to spend less than standard non contact hours planning lessons so they can cover having a reduced numbers of teachers to try to lower the significant debts. War is declared, kids education only important for hostage negotiation.
Who benefits? The business. Who loses? Pretty much everyone else, as the ripples expand outwards.
Just one tiny way of how to make money out of involvement in a school without the feared branding direct involvement, but run down the staff, pupils, and actual value of the buildings in the process.
Another is you enlarge another school (2) to take school 1's pupils even though it's not walking distance. Then close school 1, even though there's already too few places in the area and a birth boom. You then knock down school 1 and build more housing using regeneration money, creating an even bigger need for places in a few years, but no available site for a school.
(for anyone who cares, something similar?s being done with many HA properties as well)