When Alexander the Greek conquered most of the known world, he sought to spread Greek culture, also known as Hellenism, throughout his kingdom. With the onslaught of Hellenism, the Jews sought to reconcile Judaism and Greek philosophy to provide a way for Judaic thought to survive. Philo Judaeus (20 BCE-50 CE) of Alexandria provides a notable example in his writing. He “employed the method of allegorical interpretation. In this method, each element of a story or narrative is understood to have some symbolic significance that points to a greater truth.”  He was successful in utilizing this method to merge the Law of Moses with the philosophy of the Greeks. “While Philo and the hellenized aristocracy of the pre-Maccabbean period represent an extreme of Jewish Hellenism, it can hardly be denied that even the most orthodox of Palestine's citizens were touched by its pervasive intellectual climate.”  The Hellenistic “philosopher wanted logical answers to the questions of life. They dared to think in abstract concepts instead of dealing only with physical objects. Jewish scholars embraced these methods, falling under the persuasion that Greek logic would help them untangle the complex traditions of the rabbis.” 
The Jews also adopted the premise that “the Old Testament, leastwise, the Law of Moses was directly and totally from God; and if so, its form also - its letters - must be authentic and authoritative. Thus, much was available on the surface, and for all to examine. But the student must search deeper into it, his senses, as it were, quickened by Greek criticism; he must 'mediate' and penetrate into the Divine mysteries.”  It was this attitude coupled with the influence of the Hellenistic zeal for intellectual exploration that prompted development, during the middle to late Intertestament period, of a multi-level hermeneutical approach to Scripture. Edersheim provides an example of a similar type of analysis. If in Numbers 23:19 we read “God is not a man”, and in Deuteronomy 1:31 that the Lord was “as a man,” did it not imply, on the one hand, the revelation of absolute truth by God and, on the other, accommodation to those who were weak? Here, then, was the principle of a twofold interpretation of the Word of God -- the literal and the allegorical. In this approach, “the letter of the text must be held fast, and Biblical personages and histories were real. But only narrow-minded slaves of the letter would stop here; the more so, as sometimes the literal meaning alone would be tame, even absurd; while the allegorical interpretation gave the true sense, even though it might occasionally run counter to the letter.” 
It was this desire to apply a sense of logic or order to the sacred writings of the Judaic faith that led to the development of the hermeneutical system used at the time of Jesus. The genius of this system was that it was at once applicable and appropriate for all. A young child could receive instruction and teaching at one level while the rabbinical scholar could study and examine the same and gain deep insight and profound understanding. This system was based on the word “paradise” which, like many words in the ancient world, had a long and convoluted history. The term originated from ancient Indio-European languages and meant a walled or hedged garden, field, or vineyard. “The word is intended to convey privacy and inaccessibility; a rich and fertile place closed off to the general public.”  This word is found in several languages including Greek “paradeisos,” Aramaic “pardisa,” and Hebrew “pardes.” The word, “paradise,” with the literal meaning, is found in Luke 23:43, 2 Corinthians 12:3-4, and Revelation 2:7. According to Jewish belief, “the righteous and godly are received into Paradise, and dwell in the high places of that world, and see the glory of God and His holy angels. Their countenance will shine like the sun, and they will live forever.” 
An important aspect of pardes was the concept of “going around” or to “surround with siege works.” From this idea of “going around” or “surround” came the concept of a fence or hedge to serve as protection. Several Old Testament passages use “fence” as a metaphor. To those within the fence, the opportunity was available to partake of that within the boundaries of the fence. A fence or hedge denied access to those outside. In the same manner, some were given to understand rabbinical writings and to receive insight and instruction while others were denied the opportunity. The one who gave or refused this opportunity was ultimately God. A variation of this concept of pardes and the hedge was applied by the religious leaders, scribes, and Pharisees to the Law of Moses. The rabbis and scribes “compared the Law with a precious flowerbed that under no circumstances could be trodden upon; at a certain distance from it a fence was placed so that whoever broke it down, possibly unintentionally, had not yet walked upon the flowerbed.”  This “fence” around the Law was the Oral Law, also known as the Tradition of the Elders, and was very prominent in the days of Jesus.
While early aspects of this system may have contained elements of mysticism, as the following rabbinical parable dated in the first or second century reveals, Jewish scholars were familiar with the concepts of this multi-level system of hermeneutics. Jesus uses d'rash when dealing with individuals through the course of His ministry. Matthew 16:6-11 contains a good example of Jesus using this technique with His disciples. In this passage, He is applying d'rash, but the disciples are interpreting on the p'shat level. This is what led to the rebuke and explanation of what He meant. Another example of allegorical d'rash is in John 4:5-26 when Jesus speaks to the Samaritan woman at the well, and He uses the technique to introduce deeper spiritual implications into His words. Notice at the end of the conversation, He uses p'shat concerning the coming Messiah.
When Pharisees and Sadducees challenge His authority to teach, heal, and forgive, or were seeking a sign to prove His messianic claim in Luke 11:29-32, Jesus uses typological d'rash to recall a type in the Old Testament which refers to the Messiah. This and the reference to the Queen of the South and Solomon are found in d'rash teaching. In this confrontation, He refers to Jonah and his mission to Ninevah. The three days Jonah is in the belly of the great fish symbolizes the three days Jesus would be in the tomb. This is the obvious hint given in this answer, but other hints are found in His reply. In His response, He uses remez to several Old Testament passages including Jeremiah 3:8, 31:32, and Ezekiel 16:32 when referring to a wicked generation. The comment about the Queen of the South hints to 1 Kings 10:1-13 and 2 Chronicles 9:1-9 in the Old Testament. Typology d'rash “is very prominent in John; Jesus is the true temple, the antitype of the brazen serpent, the true water-giving rock, the true fiery pillar, the eschatological Moses and the new Torah, and the true Passover sacrifice.”  My book. The Sevens of John, delves into this fascinating topic.
We can see an example of Jesus using d'rash to communicate His message in John 3:1-14 when Nicodemus came to Him. Notice, when Nicodemus seemingly is unable to fathom the conversation, Jesus rebukes his lack of insight. Jesus uses d'rash when He refers to Moses in the wilderness. Another example of homiletic d'rash is found in 1 John 2:15-16 which uses Genesis 3:6 to make its point. There are three parallel thoughts in these two passages. Eve saw that the tree was good for food, which equates to the lust of the flesh. She saw it was pleasant to the eye, which corresponds to the lust of the eye and she believed it would make her wise, which parallels the pride of life in the passage written by the Apostle John.
Other examples of d'rash include Matthew 3:11 and Isaiah 40:3, Romans 5:14-21 and Genesis 3:1-24, as well as Galatians 4:24-31 and Genesis 17-22. The parts of the d'rash teaching can also be very close together (Matthew 12:18-23 and Matthew 13:3-9 or Revelations 1:20 and Revelation 1:12-16 or Revelation 17:2-8 and Revelation 17:9-18). We can classify many of the illustrations and parables of Jesus as d'rash such as The Wheat and the Tares, The Seed and the Soils, The Pearl, The Dragnet, and The Father and Two Sons. The New Testament writers also included d'rash in their teachings about Jesus. “If the New Testament explains that Jesus' sufferings correspond to those of the Servant of the Lord in Isaiah 53, this is a midrash, adapting the Biblical passage to Jesus. The New Testament contains Christian midrashim whose aim is to show that the stories of the Bible were fulfilled in the life of Jesus.” 
The last method of teaching in PaRDeS is sod, meaning secret or mysterious. One form of this teaching is the complex use of numerology, the numbers of the letters in the words, and hidden meaning of names and places that contained additional spiritual significance. Another variation of sod was such that “the 'Gematria' (geometry, calculations) allowed the interpreter to find out the numerical value of the letters in a word - the Hebrew letters, like the Roman, being also numerals, and to substitute for a word one or more which had the same numerical value.”  The more common use of sod was in mysterious or secret teachings that were unexplained at the time but revealed later.