Most of these sorts of problems can be best solved by telling us WHY - why, in this case, you want to open more than 255 file handles. If we assume for the sake of argument that you need to read one line at a time from each of thousands of files, what you could do is write a function to keep track of where you are in each file and close / open new files on a priority basis - something like the following hack:

use strict;

my $limit = 250;  ### Leaving a few for main program
my $line;

$line = readFile('inp1.txt');
$line = readFile('inp2.txt');
$line = readFile('inp3.txt');
### etc
flushFiles();

{
my %files;   ### Structure containing handle, position, etc.
my $fcount;  ### Number of open files
my $opened;  ### Sequential number to tell order opened

sub readFile {
    my $file = $_[0];
    my ($closer, $handle, $line);
    
    ### Need to open file, but too many open
    if ((!$files{$file} || !$files{$file}{'handle'}) &&
        $fcount == $limit) {
        ### Find best file to close
        $closer = (sort {
            $b->{'open'} <=> $a->{'open'} ||         ### Must be open
            $a->{'accessed'} <=> $b->{'accessed'} || ### Accessed leas
+t
            $a->{'opened'} <=> $b->{'opened'}        ### Opened earlie
+st
        } values %files)[0];
        close $closer->{'handle'};
        $closer->{'handle'} = undef;
        $closer->{'open'} = undef;
        $fcount--;
    }
    
    ### Need to open file, maybe seek old position
    if (!$files{$file}{'handle'}) {
        return if !open($handle, $file);
        $files{$file}{'handle'} = $handle;
        $files{$file}{'open'}++;
        seek($handle, $files{$file}{'position'}, 0)
            if $files{$file}{'position'};
        $files{$file}{'opened'} = ++$opened
            if !$files{$file}{'opened'};
        $fcount++;
    }
    else {
        $handle = $files{$file}{'handle'};
    }
    
    $files{$file}{'accessed'}++;    

    return if !($line = <$handle>);

    ### If we successfully read data from file
    $files{$file}{'position'} += length $line;
    return $line;
}

sub flushFiles {
    my $handle;
    for (values %files) {
        close $_->{'handle'} if $_->{'handle'};
    }
    %files = ();
    $fcount = undef;
}}
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