We study the absorption and optical bistability (OB) behavior of the superconducting phase quantum circuits in the four-level cascade and closed-loop configurations. It is shown that the OB is established in both configurations and it can be controlled by the intensity and frequency of applied fluxes. It is also demonstrated that the gain-assisted OB is generated in both configurations and can switch to the gain-assisted optical multistability (OM) only by changing the relative phase of applied fluxes in closed-loop quantum system. It is worth noting that the several significant output fluxes with negligible inputs can be seen in bistable behavior of the closed-loop configuration due to the nonlinear processing.