  We introduce a two flavor Nambu--Jona-Lasinio (NJL) model with 8-quark
interactions in the scalar and the vector channel. With the lower density
region described by the density-dependent relativistic mean field model we
construct a hybrid equation of state. We especially focus on the 4-quark vector
couplings and the 8-quark vector NJL couplings and allocate a region in this
parameter subspace where hybrid stars with masses larger than $2M_\odot$ exist.
