When processing the filenames, create a hash of array. Each "basename" like TRC_20160309_1 will have an array of extensions associated with it. You did great with test cases, I added a couple more.

You can feed your ls command into this, change <DATA> to just <> in order to read stdin. perl thisprog <yourLScommand

#usr/bin/perl
use strict;
use warnings;

my %fileBaseNames;

while (my $fullName = <DATA>)
{
   next if ($fullName =~ /^s*$/);  #skip blank lines
   
   #separate the full name into name and extension
   
   my ($name, $ext) = ($fullName =~ /(\w+)\.(\w+)/);
   push( @{ $fileBaseNames {$name} }, $ext);

}

# Each hash key of %fileBaseNames contains an array of the
# .extensions found for that name

foreach my $baseName (sort keys %fileBaseNames)
{
    my (@extensions) = @{$fileBaseNames{$baseName}};
    print "file $baseName has the extensions: @extensions\n";
    
    #code to use that for selective copy goes here...
}

=EXAMPLE printout
file TRC_20160308_1 has the extensions: PDF PL
file TRC_20160309_1 has the extensions: ARC PDF ADF
file TRC_20160310_1 has the extensions: PDF

Process completed successfully
=cut


__DATA__
TRC_20160309_1.ARC
TRC_20160309_1.PDF
TRC_20160309_1.ADF
TRC_20160308_1.PDF
TRC_20160308_1.PL
TRC_20160310_1.PDF
[download]