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]