I must admit that the desired output still leaves me puzzled, but you can reach a solution without using aliases, inheritance or possibly even multiple inheritance. Simply pass a D object as an optional parameter to C's doit() method. My solution below uses Moose, i cannot stress how incredibly useful Moose is, especially if you are considering using multiple inheritance (look into roles). Hope this helps. :)

#!/usr/bin/perl -l
package A;
use Moose;
sub doit { warn "A::doit\n" }


package B;
use Moose;
extends 'A';
sub doit {
    my ($self, $class) = @_;
    warn "B::doit\n";
    return $class ? $class->doit : $self->SUPER::doit;
}


package C;
use Moose;
extends 'B';


package D;
use Moose;
sub doit { warn "D::doit\n" }


package main;
my $c = C->new;
$c->doit( D->new );
[download]

output:

B::doit
D::doit

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)