Why not override the request method and do the change there? That way, all users of the request method will get your new request class. Also see perltoot

That is more of what I was thinking but I wasn't sure how to turn an HTTP::Response into a XXX::HTTP::Response (not liking the look of Acme::Damn). When you made your reply were you basically suggesting a combination of overriding LWP::UserAgent::request and cloning the HTTP::Response into an XXX::HTTP::Response?

package XXX::LWP::UserAgent;
use base qw(LWP::UserAgent);
sub request
{
    my $self = shift;
    my $resp = $self->SUPER::request(@_);
    return XXX::HTTP::Response::clone_from_http_response($resp);
}
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or is there perhaps some other way of avoiding duplicating LWP::UserAgent::request.

Yes, this is what I mean. As I don't know how you want to turn a HTTP::Response into your XXX::HTTP::Response, as you've kept the differences between the two well to yourself, I can't tell you any better way than to write some code that creates an XXX::HTTP::Response object from a HTTP::Response object.