Surgical procedures are traditionally performed by two or more surgeons along with staff nurses: one serves as the primary surgeon and the other as his/her assistant. Introducing surgical robots into the operating room has significantly changed the dynamics of interaction between the surgeons and with the surgical site. In this paper, we design a surgical robotic system to support the collaborative operation of multiple surgeons. This Raven IV surgical robotic system has two pairs of articulated robotic arms with a spherical configuration, each arm holding an articulated surgical tool. It allows two surgeons to teleoperate the Raven IV system collaboratively from two remote sites. To optimize the mechanism design of the Raven IV system, we configure the link architecture of each robotic arm, along with the position and orientation of the four bases and the port placement with respect to the patient's body. The optimization considers seven different parameters, which results in system configurations. We optimize the common workspace and the manipulation dexterity of each robotic arm. We study here the effect of each individual parameter and conduct a brute force search to find the optimal set of parameters. The parameters for the optimized configuration result in an almost circular common workspace with a radius of 150 mm, accessible to all four arms.