I've never used Moose, but in my limited experience, most of the cases where multiple inheritance is useful seem to be ones that basically amount to Ruby's modules/mixins system¹. Are there any examples of useful patterns that aren't covered by that?
¹in fact, under the hood, Ruby modules are classes, and mixins are multiple inheritance— it's an artificial, deliberate limitation.
That's true, when I saw Moose roles I immediately thought of Ruby's mixins. They're a little more expressive though; Moose gives you ways to interrogate roles and classes that use them in more meaningful ways (IMHO), and it's not uncommon for roles to use method modifiers (thus making roles co-exist more easily) rather than clobbering methods outright.
This is all achievable in Ruby of course, the Moose docs sort of codify it and provide sugar to make these patterns the path of least resistance.
Most cases of multiple inheritence I've seen is in non-Moose Perl code, where it's being used a little like a mixin. DBI classes and code making lots of use of meta-programming (Class::MOP stuff).
¹in fact, under the hood, Ruby modules are classes, and mixins are multiple inheritance— it's an artificial, deliberate limitation.