In this study, we propose an extended plane wave framework to ensure that the electronic structure calculations of twisted bilayer 2D material systems are practically feasible. Based on the foundations presented in Zhou et al. (2019), we extend the PW framework in the following aspects: (1) a tensor-product basis set, which adopts plane waves (PWs) in the incommensurate dimensions and a localized basis in the interlayer dimension; (2) a practical application of a novel cutoff technique that we recently developed; and (3) a quasi-band structure picture under small twist angles and weak interlayer coupling limits. Based on (1) and (2), the dimensions of the Hamiltonian matrix are reduced by approximately two orders of magnitude compared with the original framework. Moreover, (3) enables us to better organize the calculations and understand the results. As a numerical example, we study the electronic structure of a linear bilayer graphene lattice system with a magic twist angle (∼1.05°). The well-known flat bands are reproduced ensuring that their features quantitatively agreed with those obtained experimentally and via other theoretical calculations. Moreover, the extended framework has a much lower computational cost than the commensurate cell approximations and is more extendable than the traditional model Hamiltonians and tight binding models. Finally, this framework readily accommodates nonlinear models, thereby laying the foundation for more effective and accurate density functional theory (DFT) calculations.