With all the caveats of the comments above, including that it might not be allowed depending on the implementation, then it might be possible if the programs keep to their own area of the file.

open the file for read and write ('+<'), then seek to a specific position, then write. Provided the two programs do not overlap the areas of the file they are writing then it might work. You might have to pre-create the file to the correct size before running the programs.

I doubt it would be practical for text files with variable length lines.