  We examine which first order phase transitions are consistent with today's
astrophysical constraints. In particular, we explore how a well-constrained
mass-radius data point would restrict the admissible parameter space and to
this end, we employ the most likely candidates of the recent NICER limits of
PSR J0030+0451. To systematically vary the stiffness of the equation of state,
we employ a parameterizable relativistic mean field equation of state, which is
in compliance with results from chiral effective field theory. We model phase
transitions via Maxwell constructions and parameterize them by means of the
transitional pressure $p_{\rm trans}$ and the jump in energy density
$\Delta\epsilon$. This provides us with a generic setup that allows for rather
general conclusions to be drawn. We outline some regions in the $p_{\rm
trans}$-$\Delta\epsilon$ parameter space that may allow for a phase transition
identification in the near future. We also find that a strongly constrained
data point, at either exceptionally large or small radii, would reduce the
parameter space to such an extent that mass and radius become insufficient
indicators of a phase transition.
