A significant number of current industrial applications rely on web services. A cornerstone task in these applications is discovering a suitable service that meets the threshold of some user needs. Then, those services can be composed to perform specific functionalities. We argue that the prevailing approach to compose services based on the "all or nothing" paradigm is limiting and leads to exceedingly high rejection of potentially suitable services. Furthermore, contemporary models do not allow "mix and match" composition from atomic services of different composite services when binary matching is not possible or desired. In this paper, we propose a new model for service composition based on "stratified graph summarization" and "service stitching". We discuss the limitations of existing approaches with a motivating example, present our approach to overcome these limitations, and outline a possible architecture for service composition from atomic services. Our thesis is that, with the advent of Big Data, our approach will reduce latency in service discovery, and will improve efficiency and accuracy of matchmaking and composition of services.