  Many-body correlations are known to be responsible for a broad range of
fascinating physical phenomena, introducing corrections that appear elusive at
the mean-field level. An example of this is the Lifshitz transition that occurs
as the Fermi surface topology changes when {\it e.g.} Coulomb interaction
effects break into the picture. In particular, the Fermi velocity
renormalization can lead a type-II Weyl semimetal at mean-field level to become
a trivial or a type-I Dirac material when correlations are accounted for, which
is far from being obvious. In this work we scrutinize the band structure of
NiTe$_2$, a material that features a type-II Dirac point near the Fermi level
within the mean-field approach. Including GW-level correlations, our findings
showcase anisotropic corrections on the Dirac carrier velocity exceeding $100
\, \%$ enhancements, underscoring the nuanced influence of electronic
interactions in the band structure. We also consider type-II Dirac crossings in
PtSe$_2$ and PtTe$_2$ and observe that including many-body effects via GW the
band topology changes, featuring trivial topology and type-I Dirac crossings,
respectively. Our findings highlights the necessity to evaluate the many-body
effects on non-trivial bands, contributing essential insights to the broader
exploration of many-body correlation effects in type-II Dirac points of
condensed-matter systems.
