None of the things I suggested earlier would fix the problem you mentioned. After some debugging, I found that open3 defaults to using the same pipe for the child's STDOUT and STDERR. (WTF?!? I'd use open2 if I wanted to do that.)

One way around that is to vivify the handles yourself. In the tested code below, that's done using

use Symbol qw( gensym );
my ($to_child, $fr_child, $fr_child_err) = map gensym, 1..3;
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And here's the code I used for testing.

#!/usr/bin/perl

use strict;
use warnings;

use IO::Select qw( );
use IPC::Open3 qw( open3 );
use Symbol     qw( gensym );


my @cmd = (
   'perl', '-e', <<__EOI__
      use IO::Handle qw( );
      # Usually want autoflush=1 for pipes.
      STDOUT->autoflush(0);
      STDERR->autoflush(0);
      print STDERR ('a') for 1..10000;  STDERR->flush();
      print STDOUT ('b') for 1..10000;  STDOUT->flush();
      print STDERR ('c') for 1..10000;  STDERR->flush();
      print STDOUT ('d') for 1..10000;  STDOUT->flush();
__EOI__
);


{
   my ($to_child, $fr_child, $fr_child_err) = map gensym, 1..3;
   my $pid = open3($to_child, $fr_child, $fr_child_err, @cmd);

   my $sel = IO::Select->new();
   $sel->add($fr_child);
   $sel->add($fr_child_err);

   while (my @ready = $sel->can_read()) {
      foreach my $handle (@ready) {
         if ($handle == $fr_child) {
            my $bytes_read = sysread($handle, my $buf='', 1024);
            if ($bytes_read == -1) {
               warn("Error reading from child's STDOUT: $!\n");
               $sel->remove($handle);
               next;
            }
            if ($bytes_read == 0) {
               print("Child's STDOUT closed\n");
               $sel->remove($handle);
               next;
            }
            printf("%4d bytes read from child's STDOUT\n", $bytes_read
+);
         }
         elsif ($handle == $fr_child_err) {
            my $bytes_read = sysread($handle, my $buf='', 1024);
            if ($bytes_read == -1) {
               warn("Error reading from child's STDERR: $!\n");
               $sel->remove($handle);
               next;
            }
            if ($bytes_read == 0) {
               print("Child's STDERR closed\n");
               $sel->remove($handle);
               next;
            }
            printf("%4d bytes read from child's STDERR\n", $bytes_read
+);
         }
      }

      # For demonstration purposes only.
      # Should cause some STDOUT and STDERR reads to become interlaced
      use Time::HiRes qw( sleep );
      sleep(0.1);
   }

   for (;;) {
      my $pid = wait();
      last if $pid == -1;

      # Check the error code of the child process if desired.
   }
}
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