We demonstrate the selective fabrication of Ruddlesden-Popper (RP) type SrIrO3, Sr3Ir2O7, and Sr2IrO4 epitaxial thin films using pulsed laser deposition (PLD). The RP strontium iridate series is an ideal system for studying the concerted effects of electron correlation and spin-orbit interaction. Their unique physical properties susceptible to lattice distortions motivate studies in epitaxial thin film form. However, improvement in the film quality remains a challenge due to the noble metal character of iridium and the existence of the gaseous IrO3 species. Here we fabricated three different RP phases from a single SrIrO3 target by actively controlling the Ir/Sr ratio in the films. Through systematic growth studies, we identified that the growth conditions stabilizing each RP phase directly map onto the phase diagram expected from thermodynamic equilibria. This synthetic approach allows precise control over the cation stoichiometry as evidenced by the stabilization of single phase Sr3Ir2O7 for the first time, overcoming the close thermodynamic stability between neighboring RP phases. Despite the non-equilibrium nature of PLD, these results highlight the importance of thermodynamic guiding principles to strategically synthesize the targeted phase in complex oxide thin films. Show Partial Abstract