var content = CreateMultipartFormDataContent("Catalog.zip.001");
                var uploadFile = JsonConvert.DeserializeObject<UploadFile>(Put("episerverapi/commerce/import/upload/chunk", content).
                    Content.ReadAsStringAsync().Result);

                uploadId = uploadFile.UploadId;

                content = CreateMultipartFormDataContent("Catalog.zip.002");
                var file2 = Put(String.Format("episerverapi/commerce/import/upload/chunk/{0}/{1}", uploadId, (1024 * 2) * 1), content);

                content = CreateMultipartFormDataContent("Catalog.zip.003");
                var file3 = Put(String.Format("episerverapi/commerce/import/upload/chunk/{0}/{1}", uploadId, (1024 * 2) * 2), content);

                content = CreateMultipartFormDataContent("Catalog.zip.004");
                var file4 = Put(String.Format("episerverapi/commerce/import/upload/chunk/{0}/{1}", uploadId, (1024 * 2) * 3), content);

                content = CreateMultipartFormDataContent("Catalog.zip.005");
                var file5 = Put(String.Format("episerverapi/commerce/import/upload/chunk/{0}/{1}", uploadId, (1024 * 2) * 4), content);

                var complete = Post(String.Format("episerverapi/commerce/import/upload/commit/{0}", uploadId), new FormUrlEncodedContent(new List<KeyValuePair<String, String>>()));

var state = GetBackgroundTaskState(String.Format("episerverapi/commerce/import/catalog/{0}", uploadId), new FormUrlEncodedContent(new List<KeyValuePair<String, String>>())).Result

protected static MultipartFormDataContent CreateMultipartFormDataContent(string fileName)
            {
                var content = new MultipartFormDataContent();
                var filestream = new FileStream(Path.Combine(TestDataDirectory, fileName), FileMode.Open);
                content.Add(new StreamContent(filestream), "file", fileName);
                return content;
            }

protected static async Task<JobStatus> GetBackgroundTaskState(string url, FormUrlEncodedContent content)
        {
            var msg = await TestServer.HttpClient.PostAsync(url, content);
            var returnString = await msg.Content.ReadAsStringAsync();
            returnString = returnString.Replace("\"", "");
            Guid taskId;
            if (Guid.TryParse(returnString, out taskId))
            {
                return WaitForCompletion(taskId);
            }
            return null;
        }

        protected static JobStatus WaitForCompletion(Guid taskId)
        {
            const int delayIncrement = 5;
            const int maxDelay = 100;

            JobStatus status;
            var delay = 5;
            bool done = false;
            var deadline = DateTime.Now + TimeSpan.FromMinutes(30);
            var taskManager = GetInstance<JobManager>();
            do
            {
                status = taskManager.GetJob(taskId);
                if (status != null)
                {
                    done = status.State == JobMessageType.Success || status.State == JobMessageType.Error;
                }
                
                if (!done)
                {
                    Thread.Sleep(delay);
                    delay += delayIncrement;
                    if (delay > maxDelay)
                    {
                        delay = maxDelay;
                    }
                }

                if (DateTime.Now > deadline)
                {
                    throw new Exception("The requested task timed out.");
                }
            }
            while (!done);

            return status;
        }

Thanks. This is very detailed. I can't check it out just now. Based on your code it seems that all PUT methods can be uploaded in parallel? 

Yes all the parts can be in parallel and then the complete should be after they all complete