Recently, the kagome metals AV₃Sb₅ (A=K,Rb,Cs) have gained intense research interest, as they display a wide spectrum of exotic topological properties, in addition to superconductivity, charge, orbital momentum and spin density waves. 

Motivated by a plethora of experimental evidence for unconventional charge orders in the enlarged (2×2) unit-cell of the vanadium based kagome metals, we investigate the type of topological phases that can manifest within the electronic parameter space of such kagome superlattices. 

Unlike conventional theoretical approaches, we employ a recently introduced statistical method capable of constructing topological models for any generic lattice, in an unbiased way without prior knowledge of its phase diagram. 

By extracting physically meaningful information from large datasets of randomized hopping parameters for the kagome superlattice, we find possible real-space manifestations of charge and bond modulations and associated flux patterns for different topological classes. 

Our results agree with contemporary theoretical propositions and experimental observations for the AV₃Sb₅ family.

Simultaneously, we predict new higher-order topological phases that may be realized by appropriately manipulating the currently known systems.