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Composition and spectra of Galactic cosmic rays (CRs) are vital for studies of high-energy processes in a variety of environments and on different scales, for interpretation of gamma-ray and microwave observations, disentangling possible signatures of new phenomena, and for understanding of our local Galactic neighborhood. Since its launch, AMS-02 has delivered outstanding quality measurements of the spectra of antiprotons, electrons, positrons, and nuclei: H-O, Ne, Mg, Si. These measurements resulted in a number of breakthroughs, however, spectra of heavier nuclei and especially low-abundance nuclei are not expected until later in the mission. Meanwhile, a comparison of published AMS-02 results with earlier data from HEAO-3-C2 indicate that HEAO-3-C2 data may be affected by undocumented systematic errors. Utilizing such data to compensate for the lack of AMS-02 measurements could result in significant errors. In this paper we show that a fraction of HEAO-3-C2 data match available AMS-02 measurements quite well and can be used together with Voyager 1 and ACE-CRIS data to make predictions for the local interstellar spectra (LIS) of nuclei that are not yet released by AMS-02. We are also updating our already published LIS to provide a complete set from H-Ni in the energy range from 1 MeV/nucleon to ~100-500 TeV/nucleon thus covering 8-9 orders of magnitude in energy. Our calculations employ the GalProp-HelMod framework that is proved to be a reliable tool in deriving the LIS of CR antiprotons, electrons, and nuclei H-O.