Precious little. In fact, you don't have to limit it to supernatural stuff. The betrayal of Jesus by Judas Iscariot, particularly as presented in the Gospel of Matthew, is entirely made up from material in the Jewish scriptures. What's left over is a messianic pretender, one of many, with an apocalyptic message, i.e. he expected the world to end in his generation. That he might have preached a way of life similar to that of the Cynic philosophers would fit well with an apocalyptic withdrawal from the world.
My view of any historical Jesus is that he served as a mannikin upon which to hang stories and philosophies like so much fancy clothing. Those of Paul's letters considered genuine, an in particular, Galatians, seem plausible to me. They present a Jewish sect, followers of a failed messianic pretender, essentially hijacked by Paul, to create a new religion. To this nascent religion accrued a blend of Jewish and Gentile stories. I would suspect that Paul's initial proselytes were mainly hellenized Jews
This is in essence the "classical" Christ Myth theory presented by Drews, Robertson, Remsburg, and others of that time:
"In wide circles the doubt grows as to the historical character of
the picture of Christ given in the Gospels. (...) If in spite of this anyone thinks that besides the latter a Jesus cannot also be dispensed with, this can naturally not be opposed;
but we know nothing of Jesus. Even in the representations of historical theology, he is scarcely more than the shadow of a shadow. Consequently it is self-deceit to make the figure of this 'unique' and 'mighty' personality, to which a man may believe he must on historical grounds hold fast, the central point of religious consciousness." (Drews, Arthur (1910) The Christ Myth)
"The myth theory is not concerned to deny such a possibility [that Jesus existed as a flesh and blood man].
What the myth theory denies is that Christianity can be traced to a personal founder who taught as reported in the Gospels and was put to death in the circumstances there recorded" (Robertson, Archibald. (1946)
Jesus: Myth or History? on John Robertson)
"That a man named Jesus, an obscure religious teacher, the basis of this fabulous Christ, lived in Palestine about nineteen hundred years ago, may be true.
But of this man we know nothing. His biography has not been written. A Renan and others have attempted to write it, but have failed -- have failed because
no materials for such a work exist. Contemporary writers have left us not one word concerning him." (Remsburg)
If Jesus was some Doomsday prophet then odds are his message would have been very anti-Roman and if it was resulting in a disturbance a perfect reason for Pontius Pilate to crucify him.
But this raises a troubling issue--what if Jesus being crucified by Pontius Pilate is the
only part of the story that is historically accurate? What if the rest used Paul's visions as a baseline to make Jesus more acceptable to Roman?
But if that is the real state of things then the Gospel Jesus
is a fiction in the same way the Robin Hood and King Arthur we know are fictions.