Recent research efforts have provided hints towards the innate ability of population-based evolutionary algorithms to tackle multiple distinct optimization tasks at once by combining them into a single unified search space. On the occasion that there emerges some form of complementarity between the tasks in the unified space, multitask optimization can bring about favourable leaps in the genetic lineage through automated gene transfer, thereby leading to notably accelerated convergence characteristics. In this paper, we further emphasize the efficacy of multitasking across problems through an algorithmic realization based on a coevolutionary framework. It is contended that the mechanics of cooperative coevolution are particularly well suited for exploiting the commonalities and/or complementarities between different (yet possibly related) optimization tasks in a single multitasking environment. To this end, we label the resultant approach as coevolutionary multitasking for concurrent global optimization. Further, in order to effectively navigate continuous search spaces of varying degrees of complexity, we employ the particle swarm algorithm as a sample instantiation of a base optimizer for a real-parameter unification scheme. Based on a series of numerical experiments carried out for synthetic functions as well as real-world optimization settings in engineering design, we demonstrate the efficacy of multitask optimization as a paradigm promising enhanced productivity in future decision making processes.