The starting point of this work will be the LH20t functional shown explicitly below in eq. 2. LH20t has also been the basis for the more recent ωLH22t RSLH, and for subsequent strong-correlation-corrected LHs and RSLHs. While LH20t has been the first LH that outperformed the existing GHs for the large GMTKN55 main-group energetics suite, and it provides very promising accuracy in many other areas for ground and excited states, we have ample reason to believe that the simple t-LMF is not the optimum form one may achieve. On one hand, we can point to the still better performance of the ωB97M-V RSH or the very recent highly parameterized B22plus 27 or CF22D GHs for the same test set (several of our recent RSLHs also perform better). On the other hand, we know that the scaled t-LMF violates a number of exact constraints, such as the high-density coordinate scaling limit, 29 the one-orbital limit or the asymptotic limit. But even with an LMF that fulfills these exact constraints, we are not guaranteed to achieve higher accuracy for many quantities, due to the fact that an insufficient number of exact constraints is currently available to fix the form of a rung 4 functional in general and the LMF of an LH in particular: the middle term in eq. 1 is supposed to model left-right correlation in chemical bonds while keeping delocalization errors low.