Flat File Data Source with variable number of delimited columns

I am writing a package that will process delimited flat files that will come in one of a few different versions. Within each flat file, the number of delimited columns will be the same, but each version of the file has a different number of columns. I have tried configuring the flat file data source to expect the version with the largest number of columns, but it will then throw away rows that have less than this number of columns (warning: There is a partial row at the end of the file).

Is it possible to use a single flat file data source that will work with all of the different width files?
No.

The only thing you can do is read in each line as one big record and then maybe use substrings or something to pick apart the files.