The present work introduces a novel 2D multiscale strategy (the 2D+ approach) based on a computational homogenization formalism particularly designed for modeling multilayered plates under bending-dominated situations. Within this proposed approach, the 2D plate mid-plane constitutes the macroscopic scale, while a 1D filament-like Representative Volume Element (RVE), orthogonal to the plate mid-plane and spanning the plate thickness, represents the mesoscopic scale. Such RVE captures the non-linear mechanical behavior throughout the plate thickness at each integration point of the 2D plate discretization. The chosen kinematics and discretization at the considered scales are particularly selected to 1) effectively capture relevant aspects of non-linear mechanical behavior in multilayered plates under bending-dominated scenarios, 2) achieve affordable computational times (computational efficiency), and 3) provide accurate stress distributions compared to the corresponding high-fidelity 3D simulations (computational accuracy). A first order computation homogenization multiscale framework is devised applying the Hill-Mandel principle which establishes a mechanical energy equivalence in the macro and meso scales. This links the 2D macroscopic plate and the set of 1D mesoscopic filaments, in a weakly-coupled manner, and yields remarkable computational savings in comparison with standard 3D modeling. Additionally, solving the resulting RVE problem in terms of the fluctuating displacement field allows the enforcement of an additional condition: fulfillment of linear momentum balance (equilibrium equations). This results in a physically meaningful 2D-like computational setting, in the considered structural object (multilayered plates in bending-dominated situations), which provides accurate stress distributions, typical of full 3D models.