The conical band structure is the cornerstone of graphene's ultra-broadband optical conductivity. For practical use of graphene in nonlinear photonics, however, substantial increases of the lightmatter interaction strength will be required while preserving the promising features of monolayers, as the interaction of light with a single atomic layer is limited due to the extremely short interaction length and low density of state, particularly for the long-wavelength region. Here, we report that this demand can be fulfilled by random stacking of high-quality large-area monolayer graphene up to a requested number of layers, which leads to the electronic interaction between layers being effectively switched off due to turbostratic disorder. The nonlinear characteristics of randomly stacked multilayer graphene (RSMG), which originates from a thermo-modulational feedback mechanism through ultrafast free-carrier heating and temperature-dependent carrier-phonon collisions, show clear improvements in the terahertz (THz) regime with increasing layer numbers, whereas as-grown multilayer graphene (AGMG) exhibits limited behaviors due to strong interlayer coupling. This controllable nonlinearity enhancement provides an ideal prerequisite for developing efficient graphene-based THz photonic devices.