Hadoop is a reference software framework supporting the Map/Reduce programming model. It relies on the Hadoop Distributed File System (HDFS) as its primary storage system. Although HDFS does not offer support for concurrently appending data to existing files, we argue that Map/Reduce applications as well as other classes of applications can benefit from such a functionality. We provide support for concurrent appends by building a concurrency-optimized data storage layer based on the BlobSeer data management service. Moreover, we modify the Hadoop Map/Reduce framework to use the append operation in the ''reduce'' phase of the application. To validate this work, we perform experiments on a large number of nodes of the Grid'5000 testbed. We demonstrate that massively concurrent append and read operations have a low impact on each other. Besides, measurements with an application available with Hadoop show that the support for concurrent appends to shared file is introduced with no extra cost, whereas the number of files managed by the Map/Reduced framework is substantially reduced.