Erotic Lives of the Superheroes" author Marco Mancassola depicts an aging gay Batman alongside various other super-heroes. The twin themes are aging and sex. Reviews have been mixed with some critiques suggesting that the author did not seem to know much about the iconic characters he is pastiching.
I can't help but wonder where trademarks come into this. I suppose there must be some kind of parody or literary merit defense. I vaguely recall a Susie Bright anthology that had a Batman story. But most presses take the safer route of using only original superheros, not those belonging to Marvel or DC.