Perhaps the append method will do what you want. From the CGI docs (see "Setting the value(s) of a named parameter"):

$query->param('foo','an','array','of','values');
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This sets the value for the named parameter 'foo' to an array of values. This is one way to change the value of a field AFTER the script has been invoked once before.

param() also recognizes a named parameter style of calling described in more detail later:

$query->param(-name=>'foo',-values=>['an','array','of','values']);
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As a bonus, you don't have to break object encapsulation. :-)