The continuous progress of reservoir monitoring technology provides encouraging capacities to reduce uncertainties in the subsurface characterization and to mitigate risks in field development applying the reservoir simulation approach. However, it is always challenging to take full advantage of the observation data, since an accurate representation of strong heterogeneities requires a high-resolution grid. Most of the discretization methods cannot handle full tensor permeability, and high nonlinearity introduced by complex physical process drastically reduces simulation efficiency. In this work, we develop an advanced parallel framework for reservoir simulation with the implementation of state of the art discretization and linearization methods. We apply the multipoint flux approximation (MPFA) method to handle the full tensor permeability in unstructured grids. To keep the fidelity of the geological model and improve computational efficiency, we use massively parallel computations via Message Passing Interface (MPI). Complex subsurface physics is described by mass-based formulations making the framework flexible for general-purpose reservoir simulation. However, the representation of phase behavior introduces additional workload when compared with the phase-based formulations in the traditional approach. Here, we apply the Operator-Based Linearization (OBL) approach which not only overcomes this drawback but also turns it to an advantage. In this method, the conservation equations are described in an operator form. By constructing a library of tabulated operators, the repeated work spent on complex phase behavior and property evaluation can be significantly reduced. We benchmark the parallel framework with analytical solutions under single-phase flow and multiphase flow. The results demonstrate that the parallel framework provides accurate simulation results for structured and unstructured grids. We validate that MPFA implemented in our parallel framework converges to real solutions when the permeability is a full tensor. Besides, several realistic cases have been rigorously tested confirming high computational capacity, efficiency, and accuracy of the advanced massively parallel framework for general-purpose reservoir simulation. With the implementation of MPFA and OBL approaches, the parallel framework is fully equipped for the simulation of problems with full tensor permeability, high-heterogeneities, and complex physical processes.