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Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the lowest 546 (623, 701, 745) states of the $3p^4 3d$, $3s 3p^2 3d^2$, $3s 3p^3 4p$, $3s 3p^4$, $3s^2 3d^3$, $3s^2 3p^2 3d$, $3s^2 3p^2 4d$, $3s^2 3p^2 4s$, $3p^3 3d^2$, $3p^5$, $3s 3p 3d^3$, $3s 3p^3 3d$, $3s 3p^3 4s$, $3s^2 3p 3d^2$, %$3s^2 3p^2 4f$, $3s^2 3p^2 4p$, $3s^2 3p^3$ configurations in Mn~XI (Fe~XII, Co~XIII, Ni~XIV) is provided. The comparison between calculated excitation energies for the $n=4$ states and available experimental values for Fe XII indicate that the calculations are highly accurate, with uncertainties of only a few hundred cm$^{-1}$. Lines from these states are prominent in the soft X-rays. With the present calculations, several recent new identifications are confirmed. Other identifications involving $3p^2 4d$ levels in Fe~XII that were found questionable are discussed and a few new assignments are recommended. As some $n=4$ states of the other ions also show large discrepancies between experimental and calculated energies, we reassess their identification. The present study provides highly accurate atomic data for the $n=4$ states of P-like ions of astrophysical interest, for which experimental data are scarce.