  In this work, we study the effect of (anti)kaon condensation on the
properties of compact stars that develop hypernuclear cores with and without an
admixture of $\Delta$-resonances. We work within the covariant density
functional theory with the parameters adjusted to $K$-atomic and kaon-nucleon
scattering data in the kaonic sector. The density-dependent parameters in the
hyperonic sector are adjusted to the data on $\Lambda$ and $\Xi^-$ hypernuclei
data. The $\Delta$-resonance couplings are tuned to the data obtained from
their scattering off nuclei and heavy-ion collision experiments. We find that
(anti)kaon condensate leads to a softening of the equation of state and lower
maximum masses of compact stars than in the absence of the condensate. Both the
$K^-$ and $\bar K^0$-condensations occur through a second-order phase
transition, which implies no mixed-phase formation. For large values of
(anti)kaon and $\Delta$-resonance potentials in symmetric nuclear matter, we
observe that condensation leads to an extinction of $ \Xi^{-,0}$ hyperons. We
also investigate the influence of inclusion of additional hidden-strangeness
$\sigma^{*}$ meson in the functional and find that it leads to a substantial
softening of the equation of state and delay in the onset of (anti)kaons.
