The stability criteria of rapid mass transfer and common-envelope evolution are fundamental in binary star evolution. They determine the mass, mass ratio, and orbital distribution of many important systems, such as X-ray binaries, type Ia supernovae, and merging gravitational-wave sources. We use our adiabatic mass-loss model to systematically survey intermediate-mass (IM) stars' thresholds for dynamical timescale mass transfer. The impact of metallicity on the stellar responses and critical mass ratios is explored. Both tables (Z = 0.001) and fitting formulae (Z = 0.001 and Z = 0.02) of the critical mass ratios of IM stars are provided. An application of our results to intermediate-mass X-ray binaries (IMXBs) is discussed. We find that the predicted upper limit to mass ratios, as a function of orbital period, is consistent with the observed IMXBs that undergo thermal or nuclear timescale mass transfer. According to the observed peak X-ray luminosity, L (X), we predict the range of L (X) for IMXBs as a function of the donor mass and the mass-transfer timescale.