I imagined the second solution:

my $obj = 'Parent'->new;
$obj->populate(@data);
for my $child_class (@possible_child_classes) {
    if (my $new = $child_class->new_from_parent($obj)) {
        $obj = $new;
        last
    }
}
# Don't forget to handle the case that $obj hasn't changed.
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In fact, the only problem why this shouldn't go to the parent class is the array of possible child classes. So, get it from outside; the parent can insist on its children implementing a method:

sub new_from_parent { die "Should be overriden.\n" }

sub rebless {
    my $self = shift;
    my @possible_child_classes = @_;
    for my $child_class (@possible_child_classes) {
        # etc. using $self instead of $obj.
[download]

And the code becomes

my $obj = 'Parent'->new;
$obj->populate(@data);
$obj->rebless(@possible_child_classes);
[download]