  We investigate the implications of a hypothetical $2.5\,\mathrm{M_\odot}$
neutron star in regard to the possibility of a strong phase transition to quark
matter. We use equations of state (EoS) of varying stiffness provided by a
parameterizable relativistic mean filed model transitioning in a first order
phase transition to quark matter with a constant speed of sound. We find a
strong connection between the discontinuity in energy density and the maximal
mass generated by the EoS. We demonstrate, that high maximal masses cannot be
realized for large discontinuities in energy density, which are necessary for
visible twin stars, especially for soft EoSs. As a result twin stars and
maximal masses of $M_{max}\gtrsim2.2\,M_\odot$ are mutually exclusive.
