Quote Originally Posted by Pippynip View Post
when is "быть" added?
I would look at it from a different angle. It's not a matter of when "быть" is added to "может", but of when "быть" is omitted from "может быть".
"Может", generally, doesn't mean "maybe", but it does, if people omit "быть" from "может быть" when the meaning is clear.

- Может, пойдём завтра в кино?
- Может. Что-то стоящее идёт?