Using computational fluid dynamic (CFD) simulations, based on an improved conservative level set method we investigated the dynamics of mechanically interacting fluid drops in closely packed drop systems under simple shear flow. Our 2D simulations show drop concentration (psi) as a key factor, in addition to capillary number (Ca) in controlling the two competing processes: breakup and coalescence. For a given psi, the breakup process governs the drop dynamics when Ca exceeds a critical value (Ca-c); this is replaced by the coalescence process as Ca < Ca-c. The Ca-c value is found to increase non-linearly with psi. We observed varying modes of breakup as a function of psi for different Ca values. Low concentrations (psi similar to 0) give rise to drop breakup by mid-point pinching, forming smaller daughter drops of nearly equal size. Increasing psi transforms this breakup mode into another mode characterized by asymmetric capillary instability at the drop edges. On the other hand, high Ca promotes the capillary instability to develop uniformly in strongly flattened drops, resulting in their homogeneous breakup. We demonstrate that these three modes: mid-point pinching, edge breakup and homogeneous breakup yield characteristic drop size distributions (DSDs). Our multiple drop models provide a concentration limit (psi < 0.4) for the breakup process; this is taken over by coalescence drop dynamics as psi exceeds this limit. It is shown that two contrasting mechanisms: tension-driven interfacial burst and compression-driven interfacial wave instability operate in the coalescence processes under low (Ca < 0.2) and high (Ca > 0.2) capillary numbers, respectively under high concentrations (psi > 0.4). The first coalescence mechanism develops a single bridge between two adjoining drops, which grows in diameter non-linearly with time. We predict distinctive non-linear relations for collision and pull-apart drop configurations. We finally synthesize the breakup and coalescence mechanisms in a psi - Ca space. (C) 2018 Elsevier Ltd. All rights reserved.