Hi Kal,
Here is my opinion about the classification of sentences according to structure. In most of my readings, both the old books in grammar and the new ones, sentences are structurally classified into four types: simple, compound, complex, and compound complex. Should there be an additional type, elliptical structure, for me, best fits in the classification. With all honesty, I haven't read his books yet, but I'll still give you my point of view about the concern. Let's focus on the complex sentence definition.
A COMPLEX SENTENCE consists of ONE INDEPENDENT CLAUSE and ONE or MORE DEPENDENT CLAUSES.
Let's review what a dependent clause is. Recall that an independent clause is a sentence, whereas dependent is not. A dependent clause can be a noun clause, an adjective clause, or an adverbial clause.
At this point, I want you to focus on the sentence provided by you and the improved version given by Ms Sullivan. Let's analyze the sentence guided by the complex sentence definition.
"Now, the popular kids were pursuing those that once pursued them that they had rejected in the past."
"Now, the boy was buying cars that needed parts that were difficult to find"
Accordingly, A COMPLEX SENTENCE consists of ONE INDEPENDENT CLAUSE and ONE or MORE DEPENDENT CLAUSES.
The main clauses in the sentences given are:
A. Now, the popular kids were pursuing those.
B. Now, the boy was buying cars.
The dependent clauses are:
A. 1. that once pursued them
2. that they had rejected in the past
B. A. that needed parts
B. that were difficult to find
Regardless of how many dependent clauses a sentence contains and how they are structured, as long as there is one independent clause, the sentence is a complex sentence. The definition does not restrict the structure to dependent clauses subordinated to independent clauses. Please note that the adjective/relative clauses needs to be placed as close as possible to the word/s they modify. It's just how the way it is.
Not yet convinced? Let's try to analyze Mr Bremner stands. In his book he maintains that there is a complex - complex sentence structure wherein a dependent clause is subordinated to another dependent clause. I'm just quite wondering why he did not propose another classification wherein there are 2 independent clauses, each containing one or more dependent clauses.
Maria reads the book that I gave her on her birthday and she plans to finish reading it on the 1st of November which is a holiday.
Let's analyze this.
Main Clause: Maria reads the book
She plans to finish reading it on the 1st of November.
Dependent Clause: that I gave her on her birthday
which is a holiday
Each dependent sentence above is subordinated and coordinated.
Can I call such a structure as a Compound - Complex - Complex sentence, the same way how Mr. Bremner arrive at the complex - complex structure name/classification?
Another example would be:
"I looked for Mary and Samantha at the bus station which is near Mcdonald, but they arrived at the station before noon and they left on the bus before I arrived.
Can we call this structure as Compound - Compound - Complex or Compound - Complex - Compound?
Hope this sentence analysis helps you.
P.S.
I am not a grammar expert. I just love the language.
This analysis of mine does not intend to question the authorities in the language. ☺