  We parameterize the core of compact spherical star configurations by a mass
($m_x$) and a radius ($r_x$) and study the resulting admissible areas in the
total-mass vs. total-radius plane. The employed fiducial equation-of-state
models of the corona at radii $r \ge r_x$ and pressures $p \le p_x = p(r =
r_x)$ are that (i) of constant sound velocity and (ii) a proxy of DY$\Delta$
DD-ME2 provided by Buchdahl's exactly solvable ansatz. The core ($r < r_x$) may
contain any type of material, e.g. Standard-Model matter with unspecified
equation of state or/and an unspecified Dark-Matter admixture. Employing a toy
model for the cool equation of state with first-order phase transition we
discuss also the mass-radius relation of compact stars with an admixture of
Dark Matter in a Mirror-World scenario.
