Since its launch, the Alpha Magnetic Spectrometer-02 (AMS-02) has delivered outstanding quality measurements of the spectra of cosmic-ray (CR) species,
p
¯
, e
±, and nuclei (H–Si, Fe), which resulted in a number of breakthroughs. The most recent AMS-02 result is the measurement of the spectra of CR sodium and aluminum up to ∼2 TV. Given their low solar system abundances, a significant fraction of each element is produced in fragmentations of heavier species, predominantly Ne, Mg, and Si. In this paper, we use precise measurements of the sodium and aluminum spectra by AMS-02 together with ACE-CRIS and Voyager 1 data to test their origin. We show that the sodium spectrum agrees well with the predictions made with the GalProp-HelMod framework, while the aluminum spectrum shows a significant excess in the rigidity range from 2–7 GV. In this context, we discuss the origin of other low-energy excesses in Li, F, and Fe found earlier. The observed excesses in Li, F, and Al appear to be consistent with the local Wolf-Rayet stars hypothesis, invoked to reproduce anomalous 22Ne/20Ne, 12C/16O, and 58Fe/56Fe ratios in CRs, while excess in Fe is likely connected with a past supernova activity in the solar neighborhood. We also provide updated local interstellar spectra (LIS) of sodium and aluminum in the rigidity range from a few megavolts to ∼2 TV. Our calculations employ the self-consistent GalProp-HelMod framework, which has proved to be a reliable tool in deriving the LIS of CR
p
¯
, e
−, and nuclei Z ≤ 28.