From the docs to NEXT:

NEXT.pm adds a pseudoclass named NEXT to any program that uses it. If 
+a method m calls $self-NEXT::m()>, the call to m is redispatched as i
+f the calling method had not originally been found.

In other words, a call to $self-NEXT::m()> resumes the depth-first, le
+ft-to-right search of $self's class hierarchy that resulted in the or
+iginal call to m.

[...]

Another typical use of redispatch would be in AUTOLOAD'ed methods. If 
+such a method determined that it was not able to handle a particular 
+call, it might choose to redispatch that call, in the hope that some 
+other AUTOLOAD (above it, or to its left) might do better.
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Sounds like you could use this.