Metals enhance the cooling efficiency of molecular clouds, promoting fragmentation. Consequently, increasing the metallicity may boost the formation of low-mass stars. Within the integrated galactic initial mass function (IGIMF) theory, this effect is empirically captured by a linear relation between the slope of the low-mass stellar IMF, α1, and the metal mass fraction, Z. This linear α1–Z relation has been calibrated up to ≈2 Z⊙, though higher metallicity environments are known to exist. We show that if the linear α1–Z relation extends to higher metallicities ([Z] ≳ 0.5), massive star formation is suppressed entirely. Alternatively, fragmentation efficiency may saturate beyond some metallicity threshold if gravitational collapse cascades rapidly enough. To model this behavior, we propose a logistic function describing the transition from metallicity-sensitive to metallicity-insensitive fragmentation regimes. We provide a user-friendly public code, pyIGIMF, which enables the instantaneous computation of the IGIMF theory with both linear and logistic α1–Z relations.