Graphene nanomeshes (GNM's) are garnering increasing interest due to their potential application to important technologies such as photovoltaics, chemical sensing, ion-filtration, and nanoelectronics. Semiconducting GNM's with fractional eV band gaps are good candidates for graphene-based electronics, provided that a mechanism for their stable and controlled doping is developed. Recent work has shown that controlled passivation of the edges of subnanometer pores and subsequent doping give rise to n- and p-doped GNM structures. However, these structures are difficult to fabricate at the nanoscale. Here, we use first principle calculations to study the effect of the pore size on the doping physics of GNM structures with larger pores that can potentially host more than a single dopant. We show that such doping mechanism is effective even for pores with relatively large radii. We also study the effect of the number of dopants per pore on doping stability. We find that stable rigid band n- and p-doping emerges in such structures even if the dopants form a nano-cluster in the pore - rigid band doping is achieved in all cases studied.