  GW170817 has provided valuable constraints on the equations of state of
merging binary neutron stars, which can be considered as the most probable
candidate for the source of gravitational waves. On the other hand, these
natural laboratories of extreme temperature and density may lead to the
estimation of some exotic matter like {deconfined quark matter in their cores}.
In this paper, we investigate the neutron star matter equation of state (EoS)
with the lowest order constrained variational (LOCV) method considering the
excluded volume effect (VLOCV) for nucleons {to} compute the tidal
deformability of binary neutron star mergers (BNSMs). Within this approach, the
size of nucleons makes the EoS {so} stiff that requires a phase transition in
order to avoid causality violation. Therefore, this phase transition {may lead}
to the appearance of the third family of compact stars {including} ``twin
star'' configurations. {Our EoS models are confronted with observations from
GW170817, GW190814, GW190425, and also NICER. We find out that regarding all
these constraints, the EoS models having the {transition}
pressure$\approx$30-100 MeV/fm$^{3}$ and the energy density discontinuity
$\Delta\varepsilon$$\lesssim$300 MeV/fm$^{3}$ are preferable.
