It would take a lot of resources and time and things to do it as well as the original story, so no. Also non-canon (not following the real story) story would be meh, considering The Last of Us had a perfect story which could easily be ruined with a non-canon story.
I suggest that they'd focus on sequel if they were intending to do one, or the story DLC.
What helps makes characters like Tess and Henry so compelling, and desired to be around still, is the fact that they are gone. Death is a mechanic in storytelling that triggers a response of affection toward characters that may have otherwise not have received such admiration. I liked Tess, don't get me wrong, but I know that I would not have wanted her along for the entire journey, if I am honest with myself and concentrate on the time she was still alive. Still, when I think about her now being dead, and Joel and Ellie both being upset by this, it makes me wish she could be heard from again.
What does the alternative story mode mean is giving a freedom to players to play the story mode again and again.
Players would like to play the story mode in co-operation with friends using different characters.
However, the origianl story restrict this kind of co-op elements.
As we completed the game once, we all knew about the original story, it won't be changed.
Therefore, the main concern should be the resources for modifying something like cutscene movies, events etc.