Without using Manager, this is my guess. I think the map operation and manager class serve two different purposes. The former orchestrates parallel computation (data parallelism) while the latter facilitates shared access to data across processes. So, I doubt Manager could help address the issue of chunk size described in the post. Also, I think the Manager could be used to share auxiliary data between processes, but I doubt if the communication cost would be lower than that of the map with initializer.

Hope this helps