Through element substitution in CuZnSnS, a class of kesterite-structured I-II-IV-VI semiconductors can be designed as novel functional materials. Using the first-principles calculations, we show that this element-substitution design is thermodynamically limited, that is, although I-II-IV-VI with I = Cu, Ag, II = Zn, Cd, Hg, IV = Si, Ge, Sn, and VI = S, Se, Te are stable quaternary compounds, those with II = Mg, Ca, Sr, Ba, IV =Ti, Zr, Hf, and VI = O are unstable against the phase-separation into the competing binary and ternary compounds. Three main phase-separation pathways are revealed. In general, we show that if the secondary II-VI or I-IV-VI phases prefer to have nontetrahedral structures, then the I-II-IV-VI semiconductors tend to phase separate. This finding can be used as a guideline for future design of new quaternary semiconductors.