Rename your B package to anything else and it works perfectly.

   use NEXT;

   package A;
   sub A::method   { print "$_[0]: A method\n";   
                            $_[0]->NEXT::method() }
   sub A::DESTROY  { print "$_[0]: A dtor\n";     
                            $_[0]->NEXT::DESTROY() }

   package Ba;
   use base qw( A );
   sub Ba::AUTOLOAD { print "$_[0]: B AUTOLOAD\n"; 
                            $_[0]->NEXT::AUTOLOAD() }
   sub Ba::DESTROY  { print "$_[0]: B dtor\n";     
                            $_[0]->NEXT::DESTROY() }

   package C;
   sub C::method   { print "$_[0]: C method\n";   
                            $_[0]->NEXT::method() }
   sub C::AUTOLOAD { print "$_[0]: C AUTOLOAD\n"; 
                            $_[0]->NEXT::AUTOLOAD() }
   sub C::DESTROY  { print "$_[0]: C dtor\n";     
                            $_[0]->NEXT::DESTROY() }

   package D;
   use base qw( Ba C );
   sub D::method   { print "$_[0]: D method\n";   
                            $_[0]->NEXT::method() }
   sub D::AUTOLOAD { print "$_[0]: D AUTOLOAD\n"; 
                            $_[0]->NEXT::AUTOLOAD() }
   sub D::DESTROY  { print "$_[0]: D dtor\n";     
                            $_[0]->NEXT::DESTROY() }

   package main;

   my $obj = bless {}, "D";

   $obj->method();         # Calls D::method, A::method, C::method
   $obj->missing_method(); # Calls D::AUTOLOAD, B::AUTOLOAD, C::AUTOLO
+AD

   # Clean-up calls D::DESTROY, B::DESTROY, A::DESTROY, C::DESTROY
---
D=HASH(0x811b15c): D method
D=HASH(0x811b15c): A method
D=HASH(0x811b15c): C method
D=HASH(0x811b15c): D AUTOLOAD
D=HASH(0x811b15c): B AUTOLOAD
D=HASH(0x811b15c): C AUTOLOAD
D=HASH(0x811b15c): D dtor
D=HASH(0x811b15c): B dtor
D=HASH(0x811b15c): A dtor
D=HASH(0x811b15c): C dtor
[download]

B has special meaning to perl and you shouldn't name any package as such.

Update: Fooled myself. Basically, what really happens is that use base qw(B C) loads up B.pm which resets @ISA to Exporter. Note that merely changing the use base qw( A ); line to @ISA = "A"; will make the code work the way you want. Of course, base will still load up B.pm and B.pm's loading will set @B::ISA but since @ISA is defined at runtime, everything will work as expected. So there you have it, base is loading up B. If you wish to not touch B.pm at all, you can switch all use base statements to just set @ISA directly or you can create a BEGIN block in which you define either $INC{"B.pm"} or $B::VERSION.