It looks like Rockstar has no intention of continuing with the GTA 5 story as the story base DLC seems to be the furthest thing on their mind.
We have seen more than a few upgrades and DLC from Rockstar for the game GTA 5 but so far, nothing for the single-player mode of the game. Fans have been hoping that Rockstar would work on a few story base DLC for the game but it looks as though Rockstar is only interested in the online multiplayer part of the game.
Fans thought that the DLC was just around the corner when some fans said that they spotted what looks like some files in the framework that indicate that a story DLC is on its way but the one of the voice actor for the game later came out to say that he knew nothing about an upcoming story base DLC.