jIH:

SorDaq vIghro' law' law', chalDaq bo'Degh law' puS

SuStel

No. You've left out the {vIleghbogh}.

There is something here I don't understand.

If we say {vIghro' law' law', bo'Degh law' puS}, then this means "the
cats are more numerous than the birds". Why can't we just place a noun
with a {-Daq} in front of the {vIghro'} and {bo'Degh}, with the
sentence acquiring the meaning "at that place the cats are more, than
the birds that are at that (the other place)" ?

Because the comparative structure does not include nouns with -Daq.

The structure is "A Q law' B Q puS," where A and B are noun phrases. Except for the specific changes given to us by Okrand, this structure is invariable. It is not "XDaq A Q law' YDaq B Q puS."

Now, noun phrases can include nouns with -Daq. For instance, SorDaq vIghro' vIleghbogh cat which I see in a tree. But *SorDaq vIghro' is not a noun phrase. It does not mean cat in a tree because the rules of noun-noun constructions do not allow us to put a type 5 noun suffix on any but the final noun.

So if you want the individual parts of a comparative sentence to refer to different places, you're going to have to do so with noun phrases. These can be very sophisticated:

SorDaq bIHtaHbogh vIghro''e' law' law' chalDaq bIHtaHbogh bo'Degh'e' law' puS
there are more cats in the tree than birds in the sky

Alternatively, depending on your emphasis, you can abandon the comparative construct altogether:

SorDaq law' vIghro'; chalDaq puS bo'Degh
there are many cats in the tree; there are few birds in the sky

There is one exception to the invariability of the comparative construction that I can think of:

QamvIS Hegh QaQ law' torvIS yIn QaQ puS
Better to die on our feet than live on our knees. (STVI and TKW)

This sentence is a disaster on many levels, and Okrand even points out in TKW that it is ungrammatical, though he only discusses the -vIS lacking a -taH. But by all the rules we know, *QamtaHvIS Hegh and *tortaHvIS yIn are not real relative clauses. Can you insert -vIS clauses into the comparative formula like that? We don't know. Nothing backs this sentence up.

-- 
SuStel
http://trimboli.name