Can we pass input schema after the Document to Binary Snap?

I’ve got a pipeline which is reading multiple files.

A simplified version is the below:

I’d need the output to contain a column with the filename of the original file.
As the file content has nothing to do with the filename, i can’t use the normal “copy / join” pattern, as the join would have to be one without condition - which would however multiply my data per input file.

CSV Parser does not seem to allow me to pass through the filename - which would in reality be the simplest and best solution.
Has anyone built something similar - or has some ideas on how to accomplish this?