There are many arguments in inorganic chemistry based on a transition from a high-spin to a low-spin configuration, for example:
- $K_{f,3} > K_{f,2}$ for $\ce{Fe(bipy)3}$ complex, because of "a considerable increase in LFSE" as the complex becomes low-spin (from Shriver and Atkins)
However, as the complex becomes low-spin there is also an increase in the pairing energy (or a decrease in the number of Fermi holes), so I don't see why the assumption above that low-spin complexes are always more stable than high-spin is necessarily true (it can just reflect a subtle balance between $\Delta$ and P with not indication of the overall change in energy).
Based on my knowledge, successive bipy ligands would only further enhance the mixing of $\mathrm{t_{2g}}$ SALCs and that is where increasing stabilization is coming from. However, I would predict that this factor would get weaker with each ligand substitution, as the energy match of the occupied $\mathrm{t_{2g}}$ and the π* of an incoming bipy becomes worse.
Perhaps, there is some non-linear dependence of the way the pairing energy is reduced as the orbitals get "smeared" over larger space (i.e. over both the metal and π-acceptors) on the number of $\ce{bipy}$ ligands?