The way I usually do this sort of thing is place the following in the base class:

package BaseClass;
use base 'CGI::Application';

sub cgiapp_init {
    my $self = shift;
    $self->run_modes('mode1_common' => \&mode1_common,
             'mode2_common' => \&mode2_common);
}
[download]

Then in the derived class I have the standard:

package DerivedClass;
use base 'BaseClass';

sub setup {
    my $self = shift;
    $self->start_mode('start');
    $self->run_modes([qw(derived_mode1 derived_mode2)]);
}
[download]

As the CGI::Application documentation for cgiapp_init states:

If implemented, this method is called automatically right before the setup() method is called. This method provides an optional initialization hook, which improves the object-oriented character- istics of CGI::Application. The cgiapp_init() method receives, as its parameters, all the arguments which were sent to the new() method.