Wet-on-wet printing is frequently used in inkjet printing for graphical and industrial applications, where substrates can be coated with a thin liquid film prior to ink drop deposition. Two drops placed close together are expected to interact via deformations of the thin viscous film, but the nature of these capillary interactions is unknown. Here, we show that the interaction can be attractive or repulsive depending on the distance separating the two drops. The distance at which the interaction changes from attraction to repulsion is found to depend on the thickness of the film and increases over time. We reveal the origin of the non-monotonic interactions, which lies in the appearance of a visco-capillary wave on the thin film induced by the drops. Using the thin-film equation, we identify the scaling law for the spreading of the waves and demonstrate that this governs the range over which the interaction is observed.