Soft mechanical metamaterials working on the basis of instability have numerous potential applications in the context of "machine materials." Controlling the onset of instability is usually required when rationally designing such metamaterials. We study the isolated and modulated effects of geometrical design and material distribution on the onset of instability in multimaterial cellular metamaterials. We use multimaterial additive manufacturing to fabricate cellular specimens whose unit cells are divided into void space, a square element, and an intermediate ligament. The ratio of the elastic modulus of the ligament to that of the square element [(EL)/(ES)] is changed by using different material types. Computational models are also developed, validated against experimental observations, and used to study a wide range of possible designs. The critical stress can be adjusted independently from the critical strain by changing the material type while keeping [(EL)/(ES)] constant. The critical strain shows a power-law relationship with [(EL)/(ES)] within the range [(EL)/(ES)]=0.1-10. The void shape design alters the critical strain by up to threefold, while the combined effects of the void shape and material distribution cause up to a ninefold change in the critical strain. Our findings highlight the strong influence of material distribution on the onset of the instability and buckling mode.