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Star formation models predict that the metal-poor initial mass function (IMF) can be substantially different from that observed in the metal-rich Milky Way. This changeover occurs because metal-poor gas clouds cool inefficiently due to their lower abundance of metals and dust. However, predictions for the metal-poor IMF to date rely on assuming solar-scaled abundances, i.e. [X/O] = 0 at all [O/H]. There is now growing evidence that elements such as C and O that dominate metal line cooling in the ISM do not follow solar scaling at low metallicities. In this work, we extend models that predict the variation in the characteristic (or the peak) IMF mass as a function of metallicity using [C/O] ratios derived from observations of metal-poor Galactic stars and of Hii regions in dwarf galaxies. These data show [C/O] < 0 at subsolar [O/H], which leads to a substantially different metal-poor IMF in the metallicity range where Ci and Cii cooling dominate ISM thermodynamics, resulting in an increase in the characteristic mass by a factor as large as 7. An important consequence of this difference is a shift in the location of the transition from a top- to a bottom-heavy IMF upwards by 0.5-1 dex in metallicity. Our findings indicate that the IMF is very sensitive to the assumptions around solar-scaled ISM compositions in metal-poor systems (e.g. dwarf galaxies, the Galactic halo, and metal-poor stars) that are a key focus of JWST.