We present a new development in the multireference covariant density functional theory (MR-CDFT) for the low-lying states of odd-mass nuclei by mixing configurations with different intrinsic quadrupole shapes and different K quantum numbers. All configurations are projected onto the good particle numbers and angular momenta. The success of this newly developed framework is illustrated in its application to the low-lying states of \(^{43}\) S near the neutron magic number \(N=28\) with shape coexistence. Our results indicate that the ground state, \(3/2^-_1\) , is predominantly composed of the intruder prolate one-quasiparticle (1qp) configuration \(\nu 1/2^-[321]\) . In contrast, the \(7/2^-_1\) state is identified as a high-K isomer, primarily built on the prolate 1qp configuration \(\nu 7/2^-[303]\) . Additionally, the \(3/2^-_2\) state is found to be an admixture dominated by an oblate configuration with \(K^\pi = 1/2^-\) , along with a small contribution from a prolate configuration with \(K^\pi = 3/2^-\) . These results demonstrate the capability of MR-CDFT to capture the intricate interplay among shape coexistence, configuration mixing, and isomerism in the low-energy structure of odd-mass nuclei around \(N = 28\) , without invoking triaxiality.
