Your data looks rather like it may be XML, in which case you may be better to look at some of the XML modules such as XML::Twig and XML::TreeBuilder. As an example of how these things can help consider:

#! /bin/perl -w
use strict;
use warnings;
use XML::TreeBuilder;

my $root = XML::TreeBuilder->new ();

$root->parse (do {local $/; <DATA>;});

my $frame_marker = 'data';
my @dataNodes = $root->look_down ('_tag', 'data');
my $nodeCount;

for my $nodeIndex (0 .. @dataNodes - 1) {
    my @strings = $dataNodes[$nodeIndex]->look_down ('_tag', 'string')
+;
    
    print "Data node " . ($nodeIndex + 1) . "\n";
    print "   ", $_->as_text (), "\n" for @strings;
}


__DATA__
<root>
<data>
  <string>1 some stuff</string>
  <string>1 some more stuff</string>
  <string>1 yet more stuff</string>
  <string>1 enough stuff</string>
</data>
<data>
  <string>2 some stuff</string>
  <string>2 some more stuff</string>
  <string>2 yet more stuff</string>
  <string>2 enough stuff</string>
</data>
<data>
  <string>3 some stuff</string>
  <string>3 some more stuff</string>
  <string>3 yet more stuff</string>
  <string>3 enough stuff</string>
</data>
</root>
[download]

Prints:

Data node 1
   1 some stuff
   1 some more stuff
   1 yet more stuff
   1 enough stuff
Data node 2
   2 some stuff
   2 some more stuff
   2 yet more stuff
   2 enough stuff
Data node 3
   3 some stuff
   3 some more stuff
   3 yet more stuff
   3 enough stuff
[download]