Error Writing Data To Same Destination In Single Data Flow

I am getting the following error running a data flow that splits the input data into multiple streams and writes the results of each stream to the same destination table:

"This operation conflicts with another pending operation on this transaction. The operation failed."

The flow starts with a single source table with one row per student and multiple scores for that student. It does a few lookups and then splits the stream (using Multicast) in several layers, ultimately generating 25 destinations (one for each score to be recorded), all going to the same table (like a fact table). This all is running under a transaction at the package level, which is distributed to a separate machine.

Apparently, I cannot have all of these streams inserting data into the same table at one time. I don't understand why not. In an OLTP system, many transactions are inserting records into the same table at once. Why can't I do that within the same transaction?

I suppose I can use a UnionAll to join them back together before writing to a single destination, but that seems like an unnecessary waste and clutters the flow. Can anyone offer a different solution or a reason why this fails in the first place?

Thanks in advance.