Not only can $\ce{Ne^{8+}}$ exist, it probably does in the Sun's corona. And we may even have $\ce{Ne^{9+}}$ there.
Coronium
During the total solar eclipse of 1769, two scientists independently discovered an element, coronium, from a green spectral line emitted by the Sun's corona. The discovery stood until the 1930s, when the line was correlated instead with iron --ionized 13 times ($\ce{Fe^{13+}}$). Other spectral lines were assigned to other heavily ionized elements such as nickel. What was actually discovered was a tremendous energy source that heats the corona to the millions of degrees needed to create such ions by thermal energy. Powerful magnetic forces are known to exist on the surface of the Sun and are believed to be the coronal energy source.
Ionization energies
A look at a table of ionization energies reveals that it takes a total of about $920$ eV to ionize neon to $\ce{Ne^{8+}}$, but the corona is able to provide at least $2040$ eV to some atoms forming coronium/$\ce{Fe^{13+}}$. So clearly if the corona can produce the former, it can also produce the latter provided that the neon exists. Evidence for such neon may be found from the occurrence of this gas in the Moon's exosphere, likely derived from the solar wind.
Encore
Now, about that $\ce{Ne^{9+}}$. If we add the ninth ionization energy of neon to the first eight which were totaled above, we get a total of about $2120$ eV to form $\ce{Ne^{9+}}$, compared with the $2040$ for the known $\ce{Fe^{13+}}$. It would therefore be not much of a reach to assume that the corona can impart the ninth ionization of neon, too.