  We analyze the impact of several multi-quark interaction channels on the
properties of hybrid stars. Four and eight vector interactions were included in
the $SU(3)$ NJL model to describe the quark matter, and all vector like
interactions were investigated. The hybrid stars were built starting from an
hadronic EoS that satisfy presently accepted nuclear matter properties and
considering the quark model constrained by the vacuum properties of several
light mesons. The interplay between the 8-quark vector interaction and the
4-quark isovector-vector interaction determine the size of the quark core and
its strangeness content. The inclusion of a isovector-vector interaction is
essential to obtain large $s$-quark contents and a smaller central speed of
sound, although this interaction pushes the onset of quarks to larger
densities. It is observed that low mass stars, with a mass below 1.4$M_\odot$,
may contain a quark core but with small strangeness content. It is shown that
the presently existing mass and tidal deformability constraints from NS
observations allow for the existence of hybrid stars with a large strangeness
content and large quark cores for binary mass ratios $q=M_2/M_1\gtrsim 0.85$.
