You want the "c3" method resolution order. There is builtin support for this activated using use mro qw( c3 );. The module also provides next::method and maybe::next::method as alternatives to SUPER::.

use strict;
use warnings;
use feature qw( say );

{ package ClsA; use mro 'c3';
  sub foo { say __PACKAGE__; } }

{ package ClsB1; use mro 'c3'; our @ISA = qw( ClsA ); }
{ package ClsB2; use mro 'c3'; our @ISA = qw( ClsA );
  sub foo { say __PACKAGE__; $_[0]->maybe::next::method() } }
{ package ClsB3; use mro 'c3'; our @ISA = qw( ClsA );
  sub foo { say __PACKAGE__; $_[0]->maybe::next::method() } }

{ package ClsD; use mro 'c3'; our @ISA = qw( ClsB1 ClsB2 ClsB3 ); }

ClsD->foo();
say "--";
ClsB2->foo();
[download]

ClsB2
ClsB3
ClsA
--
ClsB2
ClsA
[download]

Update: Added code example and then improved it.