While the previous post highlighted the most common Three Kingdoms analogies, there are many more. Most of these variant accounts are regional or founded in various subcultures across China. Note that most of these accounts are either unverified or have only been reported to me by a single source, so it is possible that they were never in common use.
-Zhuge Liang as Jesus
In this version, Liu Bei's three visits to the sage Zhuge Liang are likened to the journey of the Magi to Bethlehem. This event is one of the most famous from the novel, having been referenced in East Asian novels for centuries, and it makes for a good story. It would also allow the teacher to use Zhuge Liang's feigned death as an analogy for the resurrection. However, it is very unlikely that this story ever came into common use, given that it downplayed the importance of Liu Bei and his brothers.
-Cao Cao as a heroic figure
As mentioned before, Cao Cao was typically used as a stand-in for a villain, such as Judas or Caiaphas. However, as Cao Cao is shown as an honorable man even in the novels, some stories use him to illustrate more positive events. Several people reported to me that they have heard a particular event in Cao Cao's life used to explain the parable of the Good Samaritan. I also know of one school which used Cao Cao as an analogy for Joseph, comparing the early relationship between Cao Cao and Liu Bei to the relationship between father and son.
-Old Testament storytelling
On occasion, mimajiao was used to relate Old Testament stories. Teachers would use battles - particularly battles where a smaller force triumphed over a greater one, such as Guandu and Red Cliffs - to illustrate how the power of God allowed a weak person or group to triumph. In Old Testament mimajiao, Sun Quan is often used to stand in for King David.