Although highly unlikely, it is possible the Patrick Jane is hunting himself (Red John) with Red John as his alter ego.
I mean, John and Jane has the same personalities when it comes to mentalism.
But they are opposite in reality.

Take the two last names. JANE and JOHN. Male and Female opposites and in the police lingo always used to describe unknown victims. JANE DOE/JOHN DOE. William Blake Poem used Talks of Symmetry.
Jane is the soft side - the Female version
John is the hard side - the Male version
This could explain why Jane can never catch Red John
Also, in the final episode of season 2, Red John recites a William Blake Poem about a Tiger,
Jane orders The Lamb at the beginning. The Lamb is another poem by William Blake.
Lamb and Tiger are opposites.
Jane - Lamb - HARMLESS
John - Tiger - DANGEROUS

And both are taken from the collection: Songs of Innocence and experience. Again two opposites.
Jane - Innocent
John - Experienced.