Binary evolution is indispensable in stellar evolution to understand the formation and evolution of most peculiar and energetic objects, such as binary compact objects, Type Ia supernovae, X-ray binaries, cataclysmic variables, blue stragglers, hot subdwarfs, and central binaries in planetary nebulae. Mass transfer in binary stars can change the evolutionary path and fate of the components compared to what is expected from single stellar evolution. The critical mass ratio at which unstable mass transfer occurs is an unsolved fundamental problem in binary evolution. To resolve this issue, we construct the thermal equilibrium mass-loss model and derive critical mass ratios for both thermal-timescale mass transfer and unstable mass transfer, the latter of which occurs when the outer Lagrangian point, L2, is overfilled. Using several 3.2 M ⊙ stellar models as examples, we study the stellar response to thermal equilibrium mass loss and present the thresholds for thermal-timescale mass transfer. We study the possible mass-transfer channels of binary systems containing a 3.2 M ⊙ donor star, taking into account thermal-timescale mass transfer, unstable mass transfer through L2, and dynamical-timescale mass transfer. We repeat this simulation for a grid of donor stars with different masses (from 0.1 to 100 M ⊙ with Z = 0.02) and at different evolutionary stages, and present our results. The results show that unstable mass transfer due to the overfilling of the outer Lagrangian point may also play an essential role in the formation of common envelopes for late red giant branch and asymptotic giant branch donors.