Stellar spectral classification is a fundamental tool of modern astronomy, providing insight into physical characteristics such as effective temperature, surface gravity, and metallicity. Accurate and fast spectral typing is an integral need for large all-sky spectroscopic surveys like the SDSS and LAMOST. Here, we present the next version of PyHammer, stellar spectral classification software that uses optical spectral templates and spectral line index measurements. PyHammer v2.0 extends the classification power to include carbon (C) stars, DA white dwarf (WD) stars, and also double-lined spectroscopic binaries (SB2). This release also includes a new empirical library of luminosity-normalized spectra that can be used to flux calibrate observed spectra, or to create synthetic SB2 spectra. We have generated physically reasonable SB2 combinations as templates, adding to PyHammer the ability to spectrally type SB2s. We test classification success rates on SB2 spectra, generated from the SDSS, across a wide range of spectral types and signal-to-noise ratios. Within the defined range of pairings described, more than $95%$ of SB2s are correctly classified.