  The observations of PSR J0952-0607 and the second object in GW190814 event
indicate the possible existence of supermassive neutron stars. In this work, by
using the Constant-Sound-Speed (CSS) parametrization to describe the equation
of state (EOS) of quark matter, the constraints on the EOS parameters from
supermassive hybrid stars are investigated through the Maxwell and Gibbs
constructions. It is shown that to support a supermassive hybrid star, a lower
transition energy density, a smaller energy density discontinuity and a higher
sound speed of quark matter are favored. For the constructed hybrid star EOS
model, the maximum mass of the corresponding hybrid stars will not meet the
lower mass limit of the second object in GW190814 if the energy density
discontinuity takes a value higher than $180~{\rm MeV~fm^{-3}}$. Moreover, it
is confirmed that the supermassive neutron star observation can also rule out
the existence of twin stars as a supermassive hybrid star requires a relatively
small energy density discontinuity. Finally, we give a rough estimate of the
lower limit of the dimensionless tidal deformability of neutron stars which
ranges from 2 to 3.
