In this work, our first objective is to gain a deeper insight into the reaction mechanisms underlying the modification of chemical reactivity induced by an optical cavity. Secondly, we aim to go beyond the single-molecule limit by considering two molecules inside the cavity, examining the impact of the collective effect and intermolecular coupling on the reaction rate. To address this challenging problem, we utilize the recently developed HEOM method in twin space. This method maps the HEOM for a set of auxiliary density matrices into a time-dependent Schrödinger equation for an extended pure state wave function. Through the application of matrix product state (MPS) decomposition (also known as tensor train (TT)) of the extended wave function, and a tangent-space time propagation scheme, we significantly extend the applicability of the HEOM method to a much larger system.