Photosynthesis, the biochemical process responsible for our survival on earth, is still rife with unknowns more than half a century after its discovery. These unknowns include its modes of function and the role of the key processes taking place apart from its regenerative Calvin cycle. It seems that the knowledge of its chemical mechanism suffices plant physiologists, who usually assume that such a natural phenomenon must work in a steady state mode, where all concentrations of molecules are almost constant throughout time or if they change, they do so between definite concentrations depending on external influences like sunlight. This uncertainty prompted us to model this phenomenon in its key elements without implementing sudden changes in external factors. We were motivated to show that such a phenomenon might possess in its inherent nature a diversity in its mode of function. For instance, multiple steady states or periodic orbits might be provable for photosynthesis models. First, we considered two already proposed models for photosynthesis and we studied the behavior of the different species thoroughly upon changing the parameters. Both models focus on unfolding the role of photorespiration, seen as a hindrance toward a better yield in crops and both models had shown maximally a single positive steady state and a single stable zero steady state signifying the collapse of the cycle. In a new model, we incorporate, apart from photorespiration, the translocation of one of the Calvin cycle species beyond the chloroplast inner membrane compensated by the entry of a phosphate group into the chloroplast from the cytosol. This exchange sets a conservation quantity bounding all concentrations, something that abides with nature's order. Throughout the analysis, we use algebraic tools like the resultant and pure analytic ones like monotonicity of solutions starting from ordered initial data. The latter feature will guarantee that no stable oscillations will be present. Also we profit from the Singular Perturbation Theory to reduce our model from a four-dimensional model into a three-dimensional model with dynamics taking place over a two-dimensional manifold. We were able to discover a domain of parameters for which two positive stable steady states exist. This breaks with the tradition of many mathematical models' results, which conclude a single positive steady state and it anticipates then multiple inherent modes of photosynthesis functions.