What is a compound complement?

The question is: if there are compound subjects, compound predicates and compound sentence, why not compound complements? Many grammar books do not have such concept. In reality, we can discover the existence of such grammatical structure. The following is an example.

e.g. The only child is used to getting plenty of candy, lavish praise from grownups, and pretty much anything else he or she wants.

The phrases in bold are complements of the preposition, to. Meanwhile, they are at same level and joined with a coordinating conjunction. In this case, we can name it 'compound complement'.