Putting together some of the other suggestions in this thread, I come up with this:

my $message = '';

open(MESSAGE, '+>>', \$message) or die "no message $!";
open(WHOM, '>>&=MESSAGE') or die "no whom $!";
open(WHAT, '>>&=MESSAGE') or die "no what $!";

print WHOM "I say 'whom'\n";
print WHAT "I say 'what'\n";

my $text;
while (my $line = <MESSAGE>) {
    print $line;
    $text .= $line;
}

print $text;
__END__
I say 'whom'
I say 'what'
I say 'whom'
I say 'what'
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