The aim of this work is to understand the exchange of water between the Serra Geral aquifer system (SGAS) and Guarani aquifer system (GAS). The objectives are two-fold. First, introduce the capability of the modified self-organizing maps (MSOM) as an unbiased nonlinear approach to estimate missing values of hydrochemistry and hydraulic transmissivity associated with the SGAS, a transboundary groundwater system spanning parts of four South American countries. Second, identify areas with potential connectivity of the SGAS with the GAS based on analysis of the spatial variability of key elements and comparison with current conceptual models of hydraulic connectivity. The MSOM is employed to calculate correlations (trends) between 27 variables from 1,132 wells. Hydraulic transmissivity is calculated from specific capacity values from well-pump tests in 157 locations. Hydrochemical facies estimates appear unbiased and consistent with current conceptual-connectivity models indicating that vertical fluxes from GAS are influenced by geological structure. The MSOM provides additional spatial estimates revealing new areas with likely connections between the two aquifer systems.