How can I increase the number of photos Prompto can take?

Solution 1:

From this comment, it appears that the Snapshot Ascension skill will allow you to take up to 5 additional pictures on top of the base 10. Additionally, the Camera Strap accessory will also increase the number of photographs Prompto will be able to share with you at each rest stop by 5.

Thus, you will be able to take a maximum of 20 pictures per rest.

However, as Snapshot is a Technique that requires usage of the Tech bar that only builds during battle, 5 of your 20 pictures will always be from during a battle (as opposed to just ambient images of your group during your travels).