Do you know words which consist of three prefixes (in one word)? It's difficult to find such examples, but I've read that there are such words in English.
I found a few examples of words with two productive prefixes added to a verb composed of a Latinate prefix and another bound Latinate morpheme. Latinate prefixes are normally considered a type of prefix in English morphology.
not reconciled to some political, economic, or social change - an unreconstructed rebel; also : holding stubbornly to a particular belief, view, place, or style - an unreconstructed hard-liner
Not reconciled or converted to the current political theory or movement. ‘an unreconstructed elitist’
- Not reconciled to social, political, or economic change; maintaining outdated attitudes, beliefs, and practices.
- Not reconciled to the outcome of the American Civil War.
negative prefix un-, attaches to adjectives, productive in modern English, native and inherited from Proto-Indo-European negative prefix *n̥-.
repetitive prefix re-, attaches to verbs, productive in modern English, borrowed from French re-/ré- and its ancestor Latin re-.
Latin prepositional prefix con-, etymologically the same as the Latin independent preposition cum; borrowed and not really productive in this form in modern English, but the prefix co-, which was used in Latin as an allomorph of con- before a vowel or the letter h, is somewhat productive in modern English. There is some phonological evidence for con-'s status as a prefix in the current morpho-phonological system of English; see Greg Lee's answer to The pronunciation of words which begins 'con' and 'com'. Also, it seems likely that most English speakers would be able to recognize a boundary between "con" and "struct" in this word because each of these sequences occurs independently of the other in many other common Latinate words, such as confront, conduction and destruction, structure.
Other similar examples
unrepresentative, un-([re-(pre-sent)]-ative), if you allow the verb "present" to be analyzed as containing a prefix "pre-".
unreproducible, un-([re-(pro-duc)]-ible), if you allow the verb "produce" to be analyzed as containing a prefix "pro-".
I also found the word "unreinforced", which could be considered to be built by adding affixes to the free morpheme "force": un-([re-(i/en-[force])]-ed). As you can see, there are some spelling adjustments in the course of the derivation: the verb "enforce" is spelled with an "e" rather than an "i", but variation between "en-" and "in-" is common in spelling and doesn't necessarily signify a true morphological distinction.