We performed numerical simulations to study the response of magnetohydrodynamics (MHD) to large-scale stochastic forcing mechanisms parameterized by one parameter, 0 ≤ a ≤ 1, going from direct injection on the velocity field (a = 1) to stirring acts on the magnetic field only (a = 0). We study the multiscale properties of the energy transfer by splitting the total flux in channels mediated by (i) the kinetic nonlinear advection, (ii) the Lorentz force, (iii) the magnetic advection, and (iv) the magnetic stretching term. We further decompose the fluxes into two subchannels given by heterochiral and homochiral components in order to distinguish forward, inverse, and flux-loop cascades. We show that there exists a quasi-singular role of the magnetic forcing mechanism for a ~ 1: a small injection on the magnetic field a < 1 can strongly deplete the mean flux of kinetic energy transfer throughout the kinetic nonlinear advection channel. We also show that this negligible mean flux is the result of a flux-loop balance between heterochiral (direct) and homochiral (inverse) transfers. Conversely, both homochiral and heterochiral channels transfer energy forward for the other three channels. Cross-exchange between velocity and the magnetic field is reversed around a = 0.4, and except when a ~ 1, we always observe that heterochiral mixed velocity–magnetic energy triads tend to move energy from magnetic to velocity fields. Our study is an attempt to further characterize the multiscale nature of MHD dynamics by disentangling different properties of the total energy transfer mechanisms, which can be useful for improving subgrid modeling.