  We study theoretically the interplay of spontaneous emission and interactions
for the multiple-excited quasistationary eigenstates in a finite periodic array
of multilevel atoms coupled to the waveguide. We develop an analytical approach
to calculate such eigenstates based on the subradiant dimer basis. Our
calculations reveal the peculiar multimerization effect driven by the
anharmonicity of the atomic potential: while a general eigenstate is an
entangled one, there exist eigenstates that are products of dimers, trimers, or
tetramers, depending on the size of the system and the fill factor. At
half-filling, these product states acquire a periodic structure with all-to-all
connections inside each multimer and become the most subradiant ones.
