The proportion of fragments that would have their orbits boosted, through multiple collisions, to an orbit higher than the upper atmosphere, is trivial. Nearly every angle of collision between two objects in orbit lowers their periapses. The risk of Kessler Syndrome doesn't come from objects in upper-atmosphere orbits somehow getting boosted out through collision chains, it comes from collisions between objects already in higher orbits not strongly affected by atmospheric drag (>600km).
It can me infinite collisions. It does not matter. Conservation of momentum still applies. The system of collisions only have a finite amount of energy. And it's chaotic rather than engineered. So it's not cumulative, much more likely to happen at numerous different angles cancelling previous collision trajectories out.