I think we've all been down this path before and found our code wanting for a cleaner framework than nested if-elseif blocks. For this type of scenario, I would strongly recommend looking at CGI::Application (which I have reviewed previously here) - This module offers a very simple, but expansive object-orientated framework that provides some structured order to CGI scripts written in this manner.

The advantage which the CGI::Application interface offers is that individual "run-modes" and execution blocks can be defined, each correlating to a particular stage of your CGI interface. Using the CGI::Application "run-mode" interface, the code above could be re-written as follows - Note that some liberty has been taken with the subroutine names and the example code shortened to reflect only that snippet of code shown above:

sub setup {
    my $self = shift;
    $self->mode_param('action');
    $self->run_modes({
        'AUTOLOAD'      =>  'action_dialog',
        'add'           =>  'add_dialog',
        'add_commit'    =>  'add_commit_dialog',
        'modify'        =>  'modify_dialog',
        'modify_commit' =>  'modify_commit_dialog',
        'remove'        =>  'remove_dialog',
        'remove_commit' =>  'remove_commit_dialog'
    });
}
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Furthermore, the CGI::Application module implements methods to address the CGI and HTML::Template modules, facilitating powerfule methods for the construction of extensible web applications.

In short, I would strongly look into CGI::Application for this type of application or alternatively, some of the different web application frameworks reviewed by princepawn at Web Application Frameworks and their Templating Engines with a Comparative Study of Template and HTML::Template.

Good luck.