Thanks for fixing the formatting; however, instead of creating a new post you can just edit the original (see "How do I change/delete my post?"). Don't worry about the original (Re^2: Multidimensional hash help!): I've requested that it be reaped.

When you post, please be specific about what you're doing. In this case, I've guessed $symb refers to the Symbol column. $UniID and $TaX are unclear (there's two columns with ID and two with Taxon): UniID and TaX may be standard abbreviations where you work (or generally in your industry) but I don't work in your industry nor do most of the people here who could help you.

The number of levels of the hash shouldn't be an issue: I'm guessing another nested for loop would've accessed all the data. In the script below, I've added another level (to what I had in my previous script) and shown how to print the fields. [For future reference, you'll find logically indenting your code makes it a lot easier to read and maintain (compare your code with mine).]

Data::Dump (which I used in my previous script) is a CPAN module which you may need to install. Data::Dumper is a built-in module. I've shown usage examples of both for comparison — you'll need click on "Reveal this spoiler" to see the output.

#!/usr/bin/env perl

use strict;
use warnings;
use autodie;

use constant {
    ID         => 0,
    SYMBOL     => 1,
    TAXON_NAME => 3,
    GO_ID      => 5,
    GO_NAME    => 6,
};

my $file = './pm_1076856.tsv';
my %go_hash;

open my $fh, '<', $file;

while (<$fh>) {
    next if $. == 1;
    my @cols = split /\t/;
    $go_hash{$cols[SYMBOL]}{$cols[ID]}{$cols[TAXON_NAME]}{$cols[GO_ID]
+}
        = $cols[GO_NAME];
}

close $fh;

for my $symbol (sort keys %go_hash) {
    for my $id (sort keys %{$go_hash{$symbol}}) {
        for my $taxon_name (sort keys %{$go_hash{$symbol}{$id}}) {
            for my $go_id (sort keys %{$go_hash{$symbol}{$id}{$taxon_n
+ame}}) {
                print join("\t" => $symbol, $id, $taxon_name, $go_id,
                                    $go_hash{$symbol}{$id}{$taxon_name
+}{$go_id}
                ), "\n";
            }
        } 
    } 
}

{
    print "\nData::Dumper Output:\n";
    use Data::Dumper;
    local $Data::Dumper::Indent = 1;
    print Dumper \%go_hash;
}

print "\nData::Dump Output:\n";
use Data::Dump;
dd \%go_hash;
[download]

Output:

Symbol1    H1SXX9    Homo Sapiens    GO:0015031    protein transport
Symbol2    H1SXZ5    Homo Sapiens    GO:0003824    catalytic activity
Symbol2    H1SXZ5    Homo Sapiens    GO:0008152    metabolic process
Symbol2    H1SXZ5    Homo Sapiens    GO:0008728    GTP diphosphokinase
+ activity
Symbol2    H1SXZ5    Homo Sapiens    GO:0015969    guanosine tetraphos
+phate metabolic process
Symbol2    H1SXZ5    Homo Sapiens    GO:0016301    kinase activity
Symbol2    H1SXZ5    Homo Sapiens    GO:0016310    phosphorylation
Symbol2    H1SXZ5    Homo Sapiens    GO:0016597    amino acid binding
Symbol2    H1SXZ5    Homo Sapiens    GO:0016740    transferase activit
+y
Symbol3    H1SXZ8    Homo Sapiens    GO:0006812    cation transport
Symbol3    H1SXZ8    Homo Sapiens    GO:0008324    cation transmembran
+e transporter activity
Symbol3    H1SXZ8    Homo Sapiens    GO:0030001    metal ion transport
Symbol3    H1SXZ8    Homo Sapiens    GO:0046872    metal ion binding
Symbol3    H1SXZ8    Homo Sapiens    GO:0055085    transmembrane trans
+port
Symbol4    H1SY02    Homo Sapiens    GO:0006810    transport
Symbol4    H1SY02    Homo Sapiens    GO:0008565    protein transporter
+ activity
Symbol4    H1SY02    Homo Sapiens    GO:0015031    protein transport
Symbol5    H1SY06    Homo Sapiens    GO:0004129    cytochrome-c oxidas
+e activity
Symbol5    H1SY06    Homo Sapiens    GO:0005506    iron ion binding
[download]

Data::Dumper Output:
$VAR1 = {
  'Symbol4' => {
    'H1SY02' => {
      'Homo Sapiens' => {
        'GO:0008565' => 'protein transporter activity',
        'GO:0015031' => 'protein transport',
        'GO:0006810' => 'transport'
      }
    }
  },
  'Symbol3' => {
    'H1SXZ8' => {
      'Homo Sapiens' => {
        'GO:0008324' => 'cation transmembrane transporter activity',
        'GO:0046872' => 'metal ion binding',
        'GO:0006812' => 'cation transport',
        'GO:0030001' => 'metal ion transport',
        'GO:0055085' => 'transmembrane transport'
      }
    }
  },
  'Symbol1' => {
    'H1SXX9' => {
      'Homo Sapiens' => {
        'GO:0015031' => 'protein transport'
      }
    }
  },
  'Symbol5' => {
    'H1SY06' => {
      'Homo Sapiens' => {
        'GO:0005506' => 'iron ion binding',
        'GO:0004129' => 'cytochrome-c oxidase activity'
      }
    }
  },
  'Symbol2' => {
    'H1SXZ5' => {
      'Homo Sapiens' => {
        'GO:0016597' => 'amino acid binding',
        'GO:0015969' => 'guanosine tetraphosphate metabolic process',
        'GO:0016740' => 'transferase activity',
        'GO:0003824' => 'catalytic activity',
        'GO:0016301' => 'kinase activity',
        'GO:0008152' => 'metabolic process',
        'GO:0016310' => 'phosphorylation',
        'GO:0008728' => 'GTP diphosphokinase activity'
      }
    }
  }
};

Data::Dump Output:
{
  Symbol1 => {
               H1SXX9 => { "Homo Sapiens" => { "GO:0015031" => "protei
+n transport" } },
             },
  Symbol2 => {
               H1SXZ5 => {
                 "Homo Sapiens" => {
                   "GO:0003824" => "catalytic activity",
                   "GO:0008152" => "metabolic process",
                   "GO:0008728" => "GTP diphosphokinase activity",
                   "GO:0015969" => "guanosine tetraphosphate metabolic
+ process",
                   "GO:0016301" => "kinase activity",
                   "GO:0016310" => "phosphorylation",
                   "GO:0016597" => "amino acid binding",
                   "GO:0016740" => "transferase activity",
                 },
               },
             },
  Symbol3 => {
               H1SXZ8 => {
                 "Homo Sapiens" => {
                   "GO:0006812" => "cation transport",
                   "GO:0008324" => "cation transmembrane transporter a
+ctivity",
                   "GO:0030001" => "metal ion transport",
                   "GO:0046872" => "metal ion binding",
                   "GO:0055085" => "transmembrane transport",
                 },
               },
             },
  Symbol4 => {
               H1SY02 => {
                 "Homo Sapiens" => {
                   "GO:0006810" => "transport",
                   "GO:0008565" => "protein transporter activity",
                   "GO:0015031" => "protein transport",
                 },
               },
             },
  Symbol5 => {
               H1SY06 => {
                 "Homo Sapiens" => {
                   "GO:0004129" => "cytochrome-c oxidase activity",
                   "GO:0005506" => "iron ion binding",
                 },
               },
             },
}
[download]