  Cosmic-rays interacting with nucleons in the solar atmosphere produce a
cascade of particles that give rise to a flux of high-energy neutrinos and
gamma-rays. Fermi has observed this gamma-ray flux; however, the associated
neutrino flux has escaped observation. In this contribution, we put forward two
strategies to detect these neutrinos, which, if seen, would push forward our
understanding of the solar atmosphere and provide a new testing ground of
neutrino properties. First, we will extend the previous analysis, which used
high-energy through-going muon events collected in the years of maximum solar
activity and yielded only flux upper limits, to include data taken during the
solar minimum from 2018 to 2020. Extending the analysis to the solar minimum is
important as the gamma-ray data collected during past solar cycles indicates a
possible enhancement in the high-energy neutrino flux. Second, we will
incorporate sub-TeV events and include contributions from all neutrino flavors.
These will improve our analysis sensitivity since the solar atmospheric
spectrum is soft and, due to oscillation, contains significant contributions of
all neutrino flavors. As we will present in this contribution, these
complementary strategies yield a significant improvement in sensitivity, making
substantial progress towards observing this flux.
