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Nail lacquer formulations are multi-ingredient complex fluids with additives that affect color, smell, texture, evaporation rate, viscosity, stability, leveling behavior, consumer's sensory experience, and dried coating's decorative and wear performance. Optimizing and characterizing the formulation rheology is critical for achieving longer shelf-life, better control over the nail painting process and adhesion, continuous manufacturing of large product volumes, and increasing overall consumer satisfaction. Dispensing, bottle filling, brush application, and dripping, as well as perceived tackiness of nail polishes, all involve capillarity-driven pinching flows associated with strong extensional deformation fields. However, a significant lack of characterization of pinching dynamics and extensional rheology response of multicomponent formulations, especially particle suspensions in viscoelastic solutions, motivates this study. Here, we characterize the shear rheology response of twelve commercial nail lacquer formulations using torsional rheometry and characterize pinching dynamics and extensional rheology response using dripping-onto-substrate (DoS) rheometry protocols we developed. We visualize and analyze brush loading, nail coating, dripping from brush, sagging, and lacquer application on a nail to outline the challenges posed by free-surface flows and non-Newtonian rheology. We find that the radius evolution over time obtained using DoS rheometry displays power law exponents distinct from those exhibited in shear thinning. Both shear and extensional viscosity decrease with deformation rate. However, the extensional viscosity appears to be rate-independent at the highest rates and displays nearly an order of magnitude larger values than the high shear rate viscosity. We envision that the findings and protocols described here will help and motivate industrial scientists to design better multicomponent formulations through a better characterization and understanding of the influence of ingredients like particles and polymers on rheology, processing, and applications.