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 Δ-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 Λ and Ξ- hypernuclei data. The Δ-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 K̄0 condensations occur through a second-order phase transition, which implies no mixed-phase formation. For large values of (anti)kaon and Δ-resonance potentials in symmetric nuclear matter, we observe that condensation leads to an extinction of Ξ-,0 hyperons. We also investigate the influence of inclusion of additional hidden-strangeness σ∗ 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. © 2021 American Physical Society.