Any complex sentence, however elaborate, may be used as one of the coordinate complex clauses that make up a compound complex sentence.
1. While the king was treated at this rude rate, Cromwell, with his army, was in Scotland, obstructing the motions that were making in his favor. But on the approach of the Scots, who were much superior in number, he was forced to retire towards Dunbar, where his ships and provisions lay.—BURNET
In this compound complex sentence, both coordinate clauses are complex. In each, the main clause has two subordinate clauses attached to it separately.
2. They had seen me cut the cables and thought my design was only to let the ships run adrift or fall foul on each other. But when they perceived the whole fleet moving in order and saw me pulling at the end, they set up such a scream of grief and despair as it is almost impossible to describe or conceive. - SWIFT
In this compound complex sentence, both of the two coördinate clauses are complex. The first contains the noun clause [that] my design ... each other, used as the object of thought. The second contains two subordinate clauses, separately attached to the main clause (they set ... despair). For the infinitive cut. The infinitive to let is used as a predicate nominative. It has as its object the infinitive clause the ships ... each other, containing two infinitives, run and fall.
3. While things went on quietly, while there was no opposition, while everything was given by the favor of a small ruling junto, Fox had a decided advantage over Pitt; but when dangerous times came, when Europe was convulsed with war, when Parliament was broken up into factions, when the public mind was violently excited, the favorite of the people rose to supreme power.—MACAULAY
This compound complex sentence consists of two complex clauses, joined by the coördinate conjunction but. In each of these, the subordinate clause is compound, consisting of several coördinate adverbial clauses introduced by relative adverbs (while in the first, when in the second).
4. The clear and agreeable language of his despatches had early attracted the notice of his employers; and before the Peace of Breda he had, at the request of Arlington, published a pamphlet on the war, of which nothing is now known, except that it had some vogue at the time, and that Charles, not a contemptible judge, pronounced it to be very well written. - MACAULAY
In this compound complex sentence, the first coördinate clause is simple, the second is complex. In the second, the adjective clause of which nothing is known has dependent on it the group of words except ... well written, consisting of the preposition except and its object (the compound noun clause, that ... time, and that ... well written). This group serves as an adjective modifier of the noun nothing. The whole passage of which ... well written forms a complex adjective clause, modifying pamphlet. It to be very well written is a complement, being an infinitive clause used as the object ofpronounced.