A few years back I remember watching an anime where the main character fell asleep and woke up in a different dimension.
I forget exactly what he did there but he woke up with a girl. He could only hear the girl say one word, which he then gave to the girl. Though he can't, everyone else who hears her can understand her completely.
He goes to sleep again and finds he's in that world, but this time with the girl and someone else (if I'm correct, it was the person taking care of him). This goes on for several episodes, where they fight different enemies and get about two to three other people on their side.
The last person seems to have an extremely strong connection to that specific world. It seems like that world was not just a dream but an actual thing. I forget what happens after that, but if anyone can help put a name to this I will greatly appreciate it.