In that case you need to be smarter about recognizing records. There seems to be a line number associated with each line of a record so you can notice when the line number resets:

use warnings;
use strict;
use Data::Dump::Streamer;

my %records;
my @lines;

while (! eof (DATA) or @lines) {
    my $line = <DATA>;
    
    $line ||= ''; # Avoid a bunch of defined tests
    chomp $line;

    next unless $line =~ /^([\s\d]\d)/ or @lines;

    if (! defined $1 or $1 <= @lines) {
        # Start of new record (or last record) - save previous
        my $id = substr $lines[0], 9, 5;
        
        $records{$id} = [@lines];
        @lines = ();
    }

    push @lines, $line if length $line;
}

Dump (\%records);

__DATA__
 10101ABC000019101L0001374686047S30339  GA   &DOE    C080229CR7  7    
+00244   0000001 000000000
 2          CR7            000            060714Q                     
+        Y   0000000000 000
 3                              00030339                           3JO
+HN DOE               36
 423 MAIN STREET  ATLANTA                GA 30339
 5                                                          +000000000
+0080226I   052461  05241961
 6Additional line 1
 7and another additional line

 10101ABC000029102 N                 D                                
+3658 MAIN STREET
 2                                ATLANTA                       GA3033
+9                           0001
 3JOHN DOE                                        05241961INDV37468604
+7S
 4
 5
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