In several other packages, here's what I did. I had to actually do a Multicast to do derived columns. Then I pulled those columns together with a UNION ALL. The UNION did not require an identity. I know this because I just replicated what I've previously done.

So you should be able to just put the multiple file sources into a Data Flow task and join them together with a UNION ALL. The trick is you need the same # of columns, in that order, and have the same metadata for each column.

Easy Peasy, no identitifier required.