The merging of drops plays a key role in many processes from simple rain to complex coating applications. In technical applications, often liquids with different surface tensions merge on a substrate like inkjet printing. For a suitable set of surface tensions, one drop can form a stable wetting film that is covering the other drop. Here, we explore the dynamics of driven wetting films and show a route toward their instability when these wetting films are driven by an external source of energy, which is Marangoni stress in our case. The wetting becomes unstable via a fingering instability and can be observed in various liquid combinations. The vapor of the liquid with the lower surface tension induces a Marangoni driven flow inside the other drop that pulls the wetting film. The concentration of the driving vapor can be controlled through the spreading velocity of the corresponding drop. We use this dependence to map out the characteristics of the instability. For very high or very low spreading velocities, no instability is observed. This is summarized in a stability diagram, which has three different regimes. A detailed analysis reveals a strong coupling of the characteristics of the fingering instability to the spreading velocity. The use of the spreading velocity as a control parameter is justified by a simplified 1D model that motivates how the spreading velocity controls the concentration profile of the second liquid vapor before and at contact. The strength of the Marangoni flow that drives the instability depends on the exposure time of the sitting drop to the vapor concentration profile around the spreading drop.