This gives the final result I think you want: 
my @oldlist = map {chomp; $_} <DATA>;

my @sorted = map {$_->[2] . " " . $_->[1]}
             sort {($a->[2] cmp $b->[2]) || ($b->[1] cmp $a->[1])}
             map { [split] } @oldlist;
my @newlist = map {shift(@oldlist) . ' ' . $_} @sorted;

print join "\n", @newlist;
__DATA__
a1 p1 q5
a1 p1 q6
a1 p2 q4
a2 p3 q9
a2 p2 q8
a2 p2 q9

[download]

__OUTPUT__
a1 p1 q5 q4 p2
a1 p1 q6 q5 p1
a1 p2 q4 q6 p1
a2 p3 q9 q8 p2
a2 p2 q8 q9 p3
a2 p2 q9 q9 p2
HTH

Update: Forgot to mention my output is different from yours, I think it was a typo in your sample output, looking at your sample input.

In reply to Re: Adding Columns from Given Data by tedrek
in thread Adding Columns from Given Data by artist

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.