Is it possible to realize an inelastic collision between three projectiles coming to the collision point simultaneously from three distinct directions making 120° with each other?
My answer is, not unless at least one of the projectiles has an internal degree of freedom that can be excited during the collision, or if two of the projectiles can be released in a bound complex due to attractive interactions. The latter outcome often occurs in three-body recombination of ultracold gases, but I do not think it a result of only the unique kinematical condition you posit.
It's impossible to answer the question definitively, as it's stated. Whether the collision is elastic or inelastic does not depend on the directions of the particles, but on the properties of their interaction-among them is, whether there is any preferred direction.
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