There is/was Coro::LWP, which integrated LWP with Coro, but so far I have not found a good way to make LWP::UserAgent-based scripts parallel without rewriting them.

I am fond of using Future, but also had good success using Mojo::UserAgent. Both have APIs somewhat different from LWP::UserAgent though.

With both systems, the logic would very much like the approach you outlined above:

# Using (my own) Future::HTTP, which provides an AnyEvent::HTTP-like A
+PI

my $ua = Future::HTTP->new();

# Fire off all requests at once, rate limiting etc. is left as an exer
+cise
my @outstanding;
for my $url (@requests) {
    my $res = $ua->http_get($url)->then(sub {
        my( $body, $data ) = @_;
        # ... handle the response
        return $body
    });
    push @outstanding, $res;
};

while( @outstanding ) {
    my $body = (shift @outstanding)->get;
    ...
};
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With Mojolicious you can look at COWS::Crawler, which also implements something like the following API:

  my $crawler = COWS::Crawler->new();
  $crawler->submit_request({ method => 'GET', url => $url, info => { u
+rl => $url }} );
  while( my ($page) = $crawler->next_page ) {
      my $body = $page->{res}->body;
      my $url = $page->{req}->req->url;
      ...
  };
[download]

But all of these approaches need a real rewrite of the formerly sequential program logic into asynchronous execution.