No.
Why?
Mario came from a simpler time when stories were like, 5th in priority behind gameplay, graphics, sound and difficulty.
Now a days story is far more important.
What modern day character could have nearly as many games as Mario does without a character reboot?
None, because new characters are expected to have more of a narrative.
Who is the most recent "Mario like" character created? Pikachu... maybe?
Character "reincarnation" in the way of Mario and Link just isn't accepted anymore.
Unless it's like... Batman or something.