The MAX phases constitute a family of nanolaminated ternary carbides and nitrides renowned for their compositional versatility, as reflected in the easy formation of solid solutions with variable chemical complexity. Synthesizing MAX phase solid solutions with intentionally tailored chemical complexity can produce materials that are able to meet the property requirements of the targeted application(s). This work presents an effective strategy specifically developed to design and fabricate highly phase-pure ceramics based on chemically complex MAX phase solid solutions by sterically stabilizing their unit cells. Steric unit cell stabilization is achieved via a judicious balance of dissimilar M- and A-elements, which targets the minimization of lattice distortions. This work produced high-purity (up to 88.7 wt %) (Zr-0.8,Ti-0.2)(2)(Al,Sn,Pb)C and (Zr-0.8,Ti-0.2)(2)(Al,Sn,Pb,Bi)C 211 MAX phase solid solutions by spark plasma sintering at 1350-1500 degrees C. Molten Zn- and/or Pb-/Bi-containing intermetallics facilitated the synthesis of soft (3-5 GPa), coarse-grained (length >20 mu m, thickness >10 mu m), and damage-tolerant ceramics. Intermetallics comprising Zn, Pb, and Bi improved (a) C/carbide dissolution, (b) Sn/C diffusion, and (c) carbide wetting, thus producing a 312 (Zr-0.8,Ti-0.2)(3)(Al,Sn,Pb,Bi)C-2 MAX phase solid solution. Forming (Zr-0.8,Ti-0.2)(3)(Al,Sn,Pb,Bi)C-2 contributed to the growth of very large platelets (length >100 mu m) with a distinct (312-core)/(211-shell) morphology. Zn did not occupy the A-site, unlike Al, Sn, Pb, and Bi. Sterically balanced A-site elemental occupancies, albeit nonequimolar, alleviated lattice distortions and aided the steric stabilization of the crystal structure, whereas the chemical complexity on the A-site increased the configurational entropy of the synthesized MAX phase compounds, despite pre-existing M-site compositional restrictions, further enhancing their thermodynamic stability.