A complete 4-partite graph ${K}_{m\u2081,m\u2082,m\u2083,m\u2084}$ is called d-halvable if it can be decomposed into two isomorphic factors of diameter d. In the class of graphs ${K}_{m\u2081,m\u2082,m\u2083,m\u2084}$ with at most one odd part all d-halvable graphs are known. In the class of biregular graphs ${K}_{m\u2081,m\u2082,m\u2083,m\u2084}$ with four odd parts (i.e., the graphs ${K}_{m,m,m,n}$ and ${K}_{m,m,n,n}$) all d-halvable graphs are known as well, except for the graphs ${K}_{m,m,n,n}$ when d = 2 and n ≠ m. We prove that such graphs are 2-halvable iff n,m ≥ 3. We also determine a new class of non-halvable graphs ${K}_{m\u2081,m\u2082,m\u2083,m\u2084}$ with three or four different...