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Are there examples of creole languages that have had three or more other languages as parents without intermediate two-language creoles? If they exist, then how high is the 'or more', i.e. what is the largest n such that a direct n-language creole exists? If the answer is no, is there a fundamental reason for this?
This question is partially motivated by thinking for the reproductive part of What evolution framework best describes the change between languages over time?
I'm not quite sure what you mean by a "direct n-language creole." Creoles can and do draw their lexicon from many different sources; I would argue looking at aspects of syntax often doesn't let us identify any clear parents at all. (Berbice Dutch, a SVO language, developed from Ijo and Dutch, both SOV). So it seems that creoles from exactly two parents are not the norm, and furthermore considering different aspects of a creole's grammar/lexicon can give different answers as to what language(s) are the parents. Nonetheless, here's an attempt at answering your question from a couple points of view.
Whinnom proposed a principle of "tertiary hybridization" which states that three language groups must be in contact for a creole to form. This is perhaps best illustrated by an example: in Papua New Guinea, Motu speakers were responsible for much coastal trade; they spoke pidgin Motu with their trading partners. The Hiri Motu ("Hiri" means trade) language arose when various of the trading partners began using their common pidgin Motu as a communication device among themselves. Motu could not form the basis of a creole (so the theory goes) when actual L1 speakers of Motu were in abundance, because they would perpetuate Motu grammatical norms as opposed to allowing a novel creole grammar to flourish.
But I suspect that you are asking about creoles with a significant lexical contribution from many languages. Smith (1987, The genesis of the creole languages of Surinam, a Univ. of Amsterdam dissertation) speaks of a core of lexical material found in English-based Atlantic creoles which comes from various African languages. It was probably first amalgamated in a pidgin English spoken in African ports, then carried to the New World by slaves.
There is also Saramaccan, which is among the most "mixed" creoles known, having drawn large portions of its core vocabulary from both English and Portugese. However, it also has other European and African influences.
