We present results from a series of two-dimensional numerical experiments in which synthetic melt compositions are calculated for a system in which a thermally buoyant, off-axis mantle plume interacts with a nearby ridge axis. Spatial gradients in synthetic melt properties are compared to observed spatial gradients in geochemistry from the Easter--Salas y Gomez system in an effort to constrain the dynamics of mantle flow in off-axis plume-ridge systems. Results indicate that observed gradients in radiogenic isotopic ratios between the ridge axis and the plume require significant heating of the ambient mantle adjacent to the plume. This heating allows ambient mantle to melt off-axis but also attenuates the flow from the plume to the ridge. When increases in viscosity due to dehydration during melting are considered, spatial gradients in the geochemical properties of synthetic melts become extremely sharp, at odds with the observational data. This may indicate that viscosity increases due to dehydration are not significant in off-axis plume-ridge systems.