Is it possible to make more than one Pokémon save file?

Solution 1:

6 Saving and Erasing Data

You can only keep one saved-game file.

6 Saving and Erasing Data (Notes regarding the downloadable version)

You can copy or move your data to a different SD Card, but you cannot use such data as a backup of your save.

Source: The electronic instruction manual accessible before or during play. You can access it by pressing the Home button, and while you have Pokémon X/Y highlighted choose Manual instead of Open/Resume.

While I have not tried personally, I assume there is some way the game prevents multiple save files.

There may be illegitimate ways to gain a second save file, but these could damage your game and/or save. The easiest way is purchasing a second copy. I recommend getting X so you and your brother can help complete each other's Pokédexes.