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Here we apply the full Will-Nordtvedt version of the ParameterizedPost-Newtonian (PPN) formalism to a class of General Relativity extensions thatare based on nontrivial renormalization group (RG) effects at large scales. Wefocus on a class of models in which the gravitational coupling constant $G$ iscorrelated with the Newtonian potential. A previous PPN analysis considered aspecific realization of the RG effects, and only within theEddington-Robertson-Schiff version of the PPN formalism, which is a lesscomplete and robust PPN formulation. Here we find stronger, more precisebounds, and with less assumptions. We also consider the External PotentialEffect (EPE), which is an effect that is intrinsic to this framework anddepends on the system environment (it has some qualitative similarities to thescreening mechanisms of modified gravity theories). We find a single particularRG realization that is not affected by the EPE. Some physical systems have beenpointed out as candidates for measuring the possible RG effects in gravity atlarge scales, for any of them the Solar System bounds need to be considered.

Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity