We present a new library of semi-empirical stellar spectra that is based on the empirical Medium resolution Isaac Newton Library of Empirical Spectra (MILES) library. A new, high-resolution library of theoretical stellar spectra is generated that is specifically designed for use in stellar population studies. We test these models across their full wavelength range against other model libraries and find reasonable agreement in their predictions of spectral changes due to atmospheric α-element variations, known as differential corrections. We also test the models against the MILES and MaStar libraries of empirical stellar spectra and also find reasonable agreements, as expected from previous work. We then use the abundance pattern predictions of the new theoretical stellar spectra to differentially correct MILES spectra to create semi-empirical MILES (sMILES) star spectra with abundance patterns that differ from those present in the Milky Way. The final result is five families of 801 sMILES stars with [α/Fe] abundances ranging from -0.20 to 0.60 dex at MILES resolution (FWHM = 2.5Å) and wavelength coverage (3540.5 - 7409.6Å). We make the sMILES library publicly available.