  The IceCube Neutrino Observatory is a one-cubic-kilometer-sized neutrino
telescope deployed deep in the Antarctic ice at the South Pole. One of
IceCube's major goals is finding the origins of astrophysical high-energy
neutrinos. In 2022, IceCube identified the strongest point-like neutrino source
so far, the active galaxy NGC 1068. Analyzing 9 years of muon-neutrino data
from the Northern Sky recorded between 2011 and 2020, the emission from NGC
1068 is significant at 4.2$\,\sigma$. We present a planned extension to this
search with additional years of data. One of these years includes data from
2010 when IceCube was only partially constructed. We discuss the improvement in
sensitivity and discovery potential for neutrino point sources across the
Northern sky. We show that by building on the established analysis techniques,
previous observations could be improved, not only for NGC 1068 but for all
possible sources in the Northern sky.
