To what fraction of the speed-of-light has any multi-atom molecule (or polyatomic ion) been accelerated? Of course photons go $c$ in a vacuum, and seems there's data on electrons getting to   $0.999999999976c$ and protons to $0.99999912c$. 
For the twins paradox to be plausible, one of the twins must reach  "99.995% the speed of light" (Lorentz factor of γ = 100 ) without being atomized. However, I can't find any examples of molecules remaining stable as they are accelerated anywhere near $c$.  Given that most accelerators use magnets and/or very high static voltage (e.g. linear accelerators), both of which operate 'best' on charged things, my refined question might read: 

What is the highest fraction of $c$ a polyatomic ion has been accelerated to without it breaking up? And, if that's not more than say $.90c$, is ion break-up indeed the limitation? 

equally useful: Any idea on what some of the fastest observed polyatomic ions have been clocked at?  ( I'm picturing a measurement on something accelerated by a charged solar wind, or maybe gravity accelerated in a mostly linear manner by an interstellar process. )

Update (2015-04-19):
So, I don't really have a good answer, but the best so far is a pathetic 0.0043$c$ ...(?!?) 
These the the best 3 datapoints I've found, all from earth reference frame: 

A comet observed at 0.0018  c (  from https://astronomy.stackexchange.com/questions/1011/is-c-2012-s1-aka-ison-the-fastest-comet-on-record-to-date )
Elements in the constellation Leo at  0.0013 c  ( using the upper bound of 380 km /sec from: http://image.gsfc.nasa.gov/poetry/ask/a10552.html)
The ion CF3 a  0.0043c  (from the paper behind the paywall at: http://www.sciencedirect.com/science/article/pii/S0168583X97004138 - using that 4 MeV applied as per nucleon )

Regarding the link on lead from Anna v -  by the time the lead ions get anywhere near high fractions of c, indeed all the electrons are stripped away (http://press.web.cern.ch/press-releases/2010/11/cern-completes-transition-lead-ion-running-lhc ). Unfortunately, a lead ion (even with its electrons) isn't a polyatomic entity/ion, and it's empirical, observational support for the stability of multi-atomic entities at high fractions of c, relative to earth-reference-frame, that I'm interested to see the data on
Anyway, the best of the above is coming in at .0043c. Since I, somehow, can't imagine that's right, if anyone can do better, or could validate that that is even approximately correct, I'd check it as the answer!
 A: Several misconceptions in your question. Let's focus on one statement:
"For the twins paradox to be plausible, one of the twins must reach "99.995% the speed of light" (Lorentz factor of γ = 100 ) without being atomized."
No. That's not true, for several reasons. 
Firstly, it is a RELATIVE speed, and relative to the frame of reference of a cosmic ray (which is every bit as valid a viewpoint as assuming that you are stationary and the cosmic ray is moving), your whole body is travelling at 0.9999999999999999999999951 c without apparent ill effect.
Secondly, the twins paradox is framed in terms of twin people for the "drama", to use dmckee's nice term. It also applies to subatomic particles, and is observed every day in dozens of particle accelerators worldwide. There can be no doubt that moving subatomic particles experience time dilation as per the predictions of SR; it is an observational fact.
Thirdly, their are formulations of the twins paradox which do not require any acceleration.
Fourthly, the twins paradox does not require speeds close to c, it can and has been measured on aircraft travelling at 200 kph (using atomic clocks), and aircraft obviously contain polyatomic molecules. GPS satellites similarly suffer time dilation exactly as predicted, and also are polyatomic.
Fifthly, even the standard description of the "twins paradox", the travelling twin is only accelerating at 1g, which isn't enough to cause polyatomic molecules to break apart (thankfully, or else I would explode every time I jumped up and down).
I'm sorry, but the tone of your question suggests that you may be trying to "disprove" SR. Lots of luck with that, it has massive experimental support.
A: There is research on going on this

The accelerators at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) provide ions – that are electrically charged particles – of most of the chemical elements available for experiments in materials research over a wide energy range. What is quite unique in the world is the fact that even very heavy metallic ions – beside monatomic also polyatomic ions with several hundred atomic mass units – are intended to be accelerated in the HZDR’s Ion Beam Center. When such heavy particles strike a material, quite new interactions could be found between the ion beam and the solid surface. This occurs because multiple atoms of the very heavy projectile impact the solid surface at the same time on the same place resulting in an extreme energy deposition..

Here they speak of keV energies, but the interest is for materials science and they do not need the high energies available in large accelerators like the LHC.
Once a polyatomic ion beam  is produced there should be no problem in accelerating it to the highest available energy, to break up they would have to interact. 
After all they accelerate lead ions at the LHC.  Energy almost 1.4TeV per nucleon they are at 

Lead ions are accelerated to 99.9% of the speed of light .

