  Higher-order repulsive interactions are included in the three-flavor NJL
model in order to describe the quark phase of an hybrid star. The effect of
4-quark and 8-quark vector-isoscalar interactions in the stability of hybrid
star configurations is analyzed. The presence of a 8-quark vector-isoscalar
channel is seen to be crucial in generating large quark branches in the $M(R)$
diagram. This is due to its stiffening effect on the quark matter equation of
state which arises from the non-linear density dependence of the speed of
sound. This additional interaction channel allows for the appearance of a quark
core at moderately low NS masses, $\sim 1M_{\odot}$, and provides the required
repulsion to preserve the star stability up to $\sim2.1M_{\odot}$. Furthermore,
we show that both the heaviest NS mass generated, $M_{\text{max}}$, and its
radii, $R_{\text{max}}$, are quite sensitive to the strength of 8-quark
vector-isoscalar channel, leading to a considerable decrease of
$R_{\text{max}}$ as the coupling increases. This behavior imprints a
considerable deviation from the purely hadronic matter equation of state in the
$\Lambda(M)$ diagram, which might be a possible signature of the quark matter
existence, even for moderately low NS masses, $\sim 1.4\, M_\odot$. The
resulting $M(R)$ and $\Lambda(R)$ relations are in accordance with the latest
astrophysical constraints from NICER and Ligo/VIRGO observations, respectively.
