  We explore the implications of third family ($t-b-\tau$) quasi-Yukawa
unification (QYU) for collider and dark matter (DM) searches within the
framework of a supersymmetric $SU(4)_c \times SU(2)_L \times SU(2)_R$ model.
The deviation from exact Yukawa unification is quantified through the relation
$y_t : y_b : y_\tau = |1+C|:|1-C|:|1+3C|$, with $C$ being a real parameter
($|C| \leq 0.2$). We allow for the breaking of left-right symmetry both by the
soft scalar and gaugino mass parameters and obtain a variety of viable
solutions that predict the sparticle mass spectrum including LSP DM (whose
stability is guaranteed by a $Z_2$ gauge symmetry). We highlight solutions that
include an NLSP gluino with mass $\sim$ 1.3-2.5 TeV, which should be accessible
at LHC Run 3. There also exist NSLP stop solutions with masses heavier than
about 1.8 TeV, which are consistent with the LSP neutralino dark matter relic
density through stop-neutralino coannihilation. We identify A-resonance
solutions with DM mass $\sim$ 0.8 - 2 TeV, as well as bino-chargino,
bino-slepton and bino-stau co-annihilation scenarios. Finally, we also identify
Wino-like ($\sim99\%$) and Higgsino-like ($\sim99\%$) solutions whose masses
are heavier than about 1.5 TeV and 1 TeV, respectively. These solutions are
compatible with the desired dark matter relic density and testable in ongoing
and future direct detection experiments.
