  The $\Delta$-isobar degrees of freedom are included in the covariant
  density functional (CDF) theory to study the equation of state (EoS)
  and composition of dense matter in compact stars. In addition to
  $\Delta$'s we include the full octet of baryons, which allows us to
  study the interplay between the onset of delta isobars and hyperonic
  degrees of freedom. Using both the Hartree and Hartree-Fock
  approximation we find that $\Delta$'s appear already at densities
  slightly above the saturation density of nuclear matter for a wide
  range of the meson-$\Delta$ coupling constants. This delays the
  appearance of hyperons and significantly affects the gross
  properties of compact stars. Specifically, $\Delta$'s soften the
  EoS at low densities but stiffen it at high densities. This
  softening reduces the radius of a canonical $1.4 M_\odot$ star by up
  to 2~km for a reasonably attractive $\Delta$ potential in matter,
  while the stiffening results in larger maximum masses of compact
  stars. We conclude that the hypernuclear CDF parametrizations that
  satisfy the 2$M_\odot$ maximum mass constraint remain valid when
  $\Delta$ isobars are included, with the important consequence that
  the resulting stellar radii are shifted toward lower values, which
  is in agreement with the analysis of neutron star radii.
