Due to the confined intraocular space and physical constraints in tool manipulation, snake-like robots have a significant potential for use in retinal microsurgery. By enhancing the dexterity at the tool tip, not only the operable space on the retina can be enlarged, but also the delicate target tissues can be reached at an optimal angle minimizing the damage and making the operation much easier. In this study, we present an improved version of our earlier integrated intraocular snake (IRIS) robot, and combine it with another robotic assistant: the cooperatively controlled Steady-Hand Eye Robot (SHER). SHER is used to drive IRIS close to the retina with precision, while IRIS makes omnidirectional bends by combining its yaw and pitch motions and provides a significantly enhanced intraocular dexterity while holding the sclerotomy port fixed. For precise control of IRIS, its snake-like tip actuation has been characterized through experiments considering both a free tool tip and external loading at the tool tip. The workspace analysis showed ±45° yaw and pitch with excellent repeatability (±1°) despite the highly miniaturized articulated segment length (3 mm) and very thin shaft (0 0.9 mm). Our preliminary experiments in an artificial eye model have shown feasibility in reaching targets requiring bends up to 55° accurately.