The overset, or chimera, grid methodology utilizes a set of overlapping grids to discretize the solution domain. Parallel computation of the overset domain connectivity information (DCI) pose unique problems relative to the typical flow solver. The present paper investigates the parallel computation of the DCI within the context of Suggar++, a general capability for obtaining the overset domain connectivity information. Significant improvements to the donor search process are also presented that reduce the time required during the donor search phase. The effect of grid partitioning on the overset work is investigated and demonstrated to cause the work to increase. A new approach to partitioning for the overset domain connectivity assembly process is proposed and demonstrated to avoid the increase in work of the conventional partitioning. The parallel execution of Suggar++ is examined in detail and is found to provide a significantly improved parallel performance relative to the current capability in SUGGAR. Finally, a new approach to eliminate orphans in tight gap regions by having the overset grid assembly process identify solver locations to be treated as immersed boundary points is also presented.