Was Jesus tempted just three times "in the wilderness"? In which order? Faced other temptations?

Find help on this Scriptural divergence and plurality of answers --
What is the proper order of the temptations? Matthew gives one order, and Luke another. This is not a contradiction, but it is a good example of how critics operate. Neither Matthew nor Luke claim to represent the chronological sequence. Luke may have reflected on the scene from the standpoint of geography, relating the two in the wilderness first, and then the one on the temple’s pinnacle (R.C. Foster, Studies in the Life of Christ, Joplin: College Press, 1996, p. 328).

Matthew records that after the temptation on the high mountain, Jesus said, “Get thee hence, Satan” (KJV).  Matthew’s order, therefore, may be the chronological sequence, but there is no contradiction between the two inspired writers.
These inquires have to do with “what” happened. Other questions are about “how” this could have happened.
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