Based on the wording of your question, I assume you already know how to open files, and read and write to them. It sounds like determining which files to merge is the holdup, so that's what I focused on.

I hacked this together based on your example data. If you don't want to use a regex a combination of File::Basename, File::Spec, and split would accomplish the same thing.

This approach simply pulls the filenames apart and uses a hash to keep track of the path, 'group by' field, and 'part' number. After all of the filenames have been read, files to be merged are identified by looking for names that contain more than one 'part' in the array. It's quick and dirty, but gets the job done.

use strict;
use warnings;

use Data::Dumper;

my @paths = qw(
    This/is/the/full/path/file.abc.part-1.txt
    This/is/the/full/path/file.abc.part-2.txt
    This/is/the/full/path/file.abc.part-3.txt
    This/is/the/full/path/file.def.part-1.txt
    This/is/the/full/path/file.def.part-2.txt
    This/is/the/full/path/file.ghi.part-1.txt
    This/is/the/full/path/file.jkl.part-2.txt
    This/is/the/full/path/file.mno.part-5.txt
);

my %combo;

foreach my $pathfile ( @paths )
{
    if( $pathfile =~ m/^(.+file\.)(\w+?)\.(part-\d+)\.txt$/ )
    {
        push( @{ $combo{$1}{$2} }, $3 );
    }
    else
    {
        warn "$pathfile does not match expected format";
    }
}

foreach my $path ( keys %combo )
{
    foreach my $type ( keys %{ $combo{$path} } )
    {
        if( scalar @{ $combo{$path}{$type} } > 1 )
        {
            my $newfile = join( '', $path, $type, '.MERGED.txt' );
            print "These files go into $newfile:\n";
            print '   ', join( ', ', @{ $combo{$path}{$type} } ), "\n"
+;
        }
    }
}

print Dumper( \%combo );
[download]

Using the example data from the OP, this outputs:

These files go into This/is/the/full/path/file.abc.MERGED.txt:
   part-1, part-2, part-3
These files go into This/is/the/full/path/file.def.MERGED.txt:
   part-1, part-2
$VAR1 = {
          'This/is/the/full/path/file.' => {
                                             'jkl' => [
                                                        'part-2'
                                                      ],
                                             'abc' => [
                                                        'part-1',
                                                        'part-2',
                                                        'part-3'
                                                      ],
                                             'mno' => [
                                                        'part-5'
                                                      ],
                                             'def' => [
                                                        'part-1',
                                                        'part-2'
                                                      ],
                                             'ghi' => [
                                                        'part-1'
                                                      ]
                                           }
        };
[download]