Let's do it anyway!
Well, someone skipped that class and made a Batman/Superman/tentacle sex comic and -- be prepared to be shocked -- it had nothing to do with Japanese manga. This happened in the official DC universe.
Don't go celebrating, Japan. The score is still like one to 38 million.
This terribly awkward adventure begins when Superman realizes that he and Batman are both pretty stressed from all that saving-the-world nonsense they do every day, so he invites Batman over for a goddamn sleepover at the Fortress of Solitude to discuss their feelings and have pillow fights and so forth. Batman accepts, because dealing with stressful situations in an emotionally healthy way has always been a trademark of Batman.