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1. TG. Ross's description is phrased in terms of Transformational Grammar. In fact the original title of his dissertation, Contraints on Variables in Syntax, is an allusion to Chomsky's characterization of TG, since transformations are to be stated in terms of variables representing substrings of labeled bracketings. It is a remarkable fact about Ross's famous dissertation that it proposes no constraints on transformational variables at all. Presumably, that is because Ross was unable to find a satisfactory formulation. So far as I know, no one else has been able to capture the Ross constraints as constraints on transformational variables, either. I conclude that TG is unable even to describe the Ross constraints, including the CNPC, much less explain them.
2. GPSG. The GPSG theory of Gazdar and others, does offer an explanation of the Coordinate Structure Constraint, and it can describe (though not explain) the CNPC. I will give a brief outline if how this works, below. I will remark here that I am still very enthusiastic about GPSG, and I am not persuaded by Stuart Schieber's work on Swiss-German that human language is not context free. Regardless, GPSG does not explain the CNPC.
3. 2PSG. This is my own theory, which is descriptively in a primitive state, but does offer an account of why no more than one NP can be extracted from a relative clause. See my 2PSG post.

1. TG. Ross's description is phrased in terms of Transformational Grammar. In fact the original title of his dissertation, Contraints on Variables in Syntax, is an allusion to Chomsky's characterization of TG, since transformations are to be stated in terms of variables representing substrings of labeled bracketings. It is a remarkable fact about Ross's famous dissertation that it proposes no constraints on transformational variables at all. Presumably, that is because Ross was unable to find a satisfactory formulation. So far as I know, no one else has been able to capture the Ross constraints as constraints on transformational variables, either. I conclude that TG is unable even to describe the Ross constraints, including the CNPC, much less explain them.
2. GPSG. The GPSG theory of Gazdar and others, does offer an explanation of the Coordinate Structure Constraint, and it can describe (though not explain) the CNPC. I will give a brief outline if how this works, below. I will remark here that I am still very enthusiastic about GPSG, and I am not persuaded by Stuart Schieber's work on Swiss-German that human language is not context free. Regardless, GPSG does not explain the CNPC.
3. 2PSG. This is my own theory, which is descriptively in a primitive state, but does offer an account of why no more than one NP can be extracted from a relative clause. See my 2PSG post.

(... more is forthcoming ...)

A basic assumption of Relational Grammar is the "Stratal Uniqueness Law", which prohibits more than one instance of the same grammatical relation from appearing at the same level of analysis. 2PSG adopts this assumption also. I apologize for the "stratal" in the name of this principle, which I disagree with. I keep the name just to identify the theory from which I stole the idea. I think it is a deep truth about human language. In 2PSG, the SUL has the form of prohibiting more than one instance of any grammatical type in a phrase structure rule (or, rather, the counterpart of a phrase structure rule in 2PSG).

For instance, the structure of "John gives Mary a book" can be described as "S1 -> NP1 gives NP3 NP2", meaning that it is a declarative finite clause S1 with a subject NP1, a head "gives", an indirect object NP3, and a direct object NP2. The SUL prohibits multiple subjects, multiple direct objects, or any two instances of the same grammatical variable, as does the original SUL principle in Relational Grammar.

The indices 0/1/2/3 give the height in a phrase structure tree of variables such as S1, NP1, NP2, NP3, and S1 is the type of declarative finite clauses. In the above illustration, no part of the sentence is any higher than the sentence as a whole, but this needn't always be the case. Without any constraint to the contrary, we can also describe constituents containing parts less oblique than the containing constituent, such as S1 -> NP1 gives NP3 NP0 (for "John gives Mary what?" for instance). These are extraction constructions.

So finally I can come to the point. If we attempt to extract two NPs from a clause, in 2PSG they would have to be both NP0 in the clause structure, and this would violate the Stratal Uniqueness Law. This is my account of why two NPs cannot be extracted from the same clause. (For more detail of how the theory works, please see my earlier post.)

(... forthcoming ...)

In traditional linguistic analysis, case systems are described with a vertical dimension. A declension describes the morphology of nouns as having the nominative form at the top and the other case forms as "declining" away from the "upright" nominative and becoming more "oblique" as you go lower in the declension. Several contemporary theories incorporate some version of this morphological theory, but applied to phrases, rather than to words. I'm thinking of Fillmore's Case Grammar, Gruber's thematic analysis, and Postal & Perlmutter's Relational Grammar.

2PSG is such a theory, and the "2" is a reference to the second, vertical dimension of traditional declensions. The degree of obliqueness of a phrase is described with an integer suffix 0, 1, 2, or 3, where the 1, 2, 3 indexes are essentially the same as the like-named grammatical relations of Relational Grammar. Grammatical relations are attributed to phrases (S, NP, PP, ...) rather than words, but there is a correspondence between 1/2/3 and the traditional description of words as having nominative/accusative/dative case forms. (The 0 grammatical relation, which is not part of Relational Grammar, corresponds to the vocative case form.)

(... more is forthcoming ...)