use Fatal qw(open);
use constant MAXLINES => 2;
open my $i, 'data.txt';

(local $/, my ($sum, $buf)) = ( '', 0 , undef); 

while (<>) {
        $buf .= $_;
        $sum +=  tr /\n/\n/;
        next  if $sum < MAXLINES ;

        print "$buf----------";; 
        ($sum, $buf) = (0, undef );
}
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Something like this?

use warnings;
use strict;

my $linesSinceBreak = 0;

while (<DATA>)
  {
  chomp;
  $linesSinceBreak = 0, print "\n<<BreakHere\n" if ++$linesSinceBreak 
+>= 15 && ! length $_;
  print "$_\n";
  }
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$. is error prone, as one can have multiple files open in a program, but there is only one $. I would rather call input_line_number() with specific file handler.

use IO::Handle;
open(MYSELF1, "<", "test.pl");
open(MYSELF2, "<", "test.pl");
while (<MYSELF1>) {
    print "after reading from myself1: $.\n";
    if ($. % 2) {
        <MYSELF2>;
        print "after reading from myself2: $.\n";
    }
    print "returned values from input_line_number: (";
    print MYSELF1->input_line_number(), ", ";
    print MYSELF2->input_line_number(), ")\n";
}
close(MYSELF1);
close(MYSELF2);
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