Is it possible to turn a RN black hole with real r+- into one with naked singularity? Let's say we initially have a RN black hole that has $Q^2<M^2$ where $Q$ and $M$ are its charge and mass respectively. Now if a particle goes into the blackhole is it possible for the new charge mass relation to become $Q^2>M^2$? 
 A: To my knowledge, there is no rigorous proof that this is impossible, but there are various reasons to strongly believe that a process like this will never happen.


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*If you assume the universe is made up of "ordinary" matter (this means, in some sense, that matter densities are not negative), then you can derive a theorem that says that the total area of all of the black holes in the universe cannot decrease.  A process like this would convert a black hole into a naked singularity, and would therefore, violate the area theorem

*Similarly, most relativists believe some version of the cosmic censorship hypothesis, which says that, given initially normal matter, the set of processes that will produce a naked singularity is of measure zero (producing a black hole requires tuning real-valued parameters to infinite precision)

*Furthermore, if you just try to naïvely accrete charge onto a black hole, the electrostatic force at the horizon asymptotes to infinity as $Q \rightarrow M$, which will prevent the further accretion of charge

*Observationally, the signature of a naked horizon is quite different from that of a black hole, and we do not observe any compact X-ray sources consistent with a naked horizon source (though I don't think it's ruled out, observationally, either).


none of this is as rigorous as "here is the proof", but all of it indicates that the process you describe cannot happen.
A: Summarizes the reasons why you can't add charge or angular momentum to a black hole to make it super-extremal. Much of the original results came from Wald. Basically, as @Jerry Schirmer writes, the Black Hole repels additional charge, and the repulsion overcomes the gravitational attraction at the horizon where Q= M. 
http://www.physics.umd.edu/grt/taj/776b/chappell.pdf
As for adding angular momentum to an extremal Black Hole, the particle one would add will miss the Black Hole. It's the limit of adding a particle with greater and greater angular momentum to a sub-extremal Black Hole. If you try to add too much, with a high angular momentum particle, it'll simply skirt the Black Hole because of too high an impact parameter.
It's also been analyzed what happens if you have an extra fictional SU(1) charge which does not have electromagnetic interactions, the particle also can not be added to the Black Hole, it would have to have a radius bigger than the Black Hole horizon. 
https://arxiv.org/pdf/gr-qc/9406024.pdf
Wald and other have analyzed the stability of the horizons, and there have been multiple other cases analyzed and that first reference has references to a Wald report on analysis done using perturbations of the Black Hole, and none have worked to destroy the horizon (or make the Black Hole super-extremal). 
Still, there are some analysis which have used other fields for the Black Hole, particularly scalar massless and the dilaton field. Reference is https://en.m.wikipedia.org/wiki/Cosmic_censorship_hypothesis and http://iopscience.iop.org/article/10.1088/0264-9381/32/13/135021/meta. There are indeed example solutions with naked singularities, i.e., having broken the Cosmic Censorship Hypothesis. 
So, it still remains a conjecture, perhaps with some physical constraints on applicability, and people are exploring the possibilities. 
