my @loggers;  # array of file handles
my @logpids;  # array of pids for open file handles
...
  # in branch of case statement for starting a new logger:
    my $args = "whatever is appropriate...";
    my $pid = open( $loggers[@loggers], "logger_script $args |" )
        or die "can't run logger_script: $!" );
    push @logpids, $pid;
...