I think it would be exciting to get a gamemode that focuses more on the game's story and maps that provide a more linear experience, plus it would provide an opportunity for the developers to add characters that wouldn't otherwise be playable, either as common enemies or bosses. Some that come to mind are Madame Hydra, Iron Monger, Abomination and Malekith.
The PvE mode could also be directly tied into the seasons. For example, in season 1 we could have been fighting an army of vampires and eventually defeat Dracula. What other characters do you think would make for exciting boss fights or just common enemies?