Community detection has been (and remains) a very important topic in several fields. From marketing and social networking to biological studies, community detection plays a key role in advancing research in many different fields. Research on this topic originally looked at classifying nodes into discrete communities (non-overlapping communities) but eventually moved forward to placing nodes in multiple communities (overlapping communities). Unfortunately, community detection has always been a time-inefficient process, and datasets are too large to realistically process them using traditional methods. Because of this, recent methods have turned to parallelism and graph stream models, where the edge list is accessed one edge at a time. However, all these methods, while offering a significant decrease in processing time, still have several shortcomings. We propose a new parallel algorithm called community detection with seed sets (CoDiS), which solves the overlapping community detection problem in graph streams. Initially, some nodes (seed sets) have known community structures, and the aim is to expand these communities by processing one edge at a time. The innovation of our approach is that it splits communities among the parallel computation workers so that each worker is only updating a subset of all the communities. By doing so, we decrease the edge processing throughput and decrease the amount of time each worker spends on each edge. Crucially, we remove the need for every worker to have access to every community. Experimental results show that we are able to gain a significant improvement in running time with no loss of accuracy.