Like $\ce{NH4+}$ ,Is there any possibility of formation of $\ce{H4O^{2+}}$ (of tetrahedral structure)?
My theory is: it can be formed by osmosis setup where heavy acids like $\ce{H3PO4}$ or $\ce{H2S2O7}$ are passed through a semipermeable membrane like gelatinous copper ferrocyanide SPM, which allow only small ions like H+ to pass.
This then could form $\ce{H3O+}$, then its lone pair could attack the excess $\ce{H+}$ in solution to form forming $\ce{H4O^{2+}}$.
The existence of $\ce{H4O^{2+}}$ has been inferred from hydrogen/deuterium isotopic exchange monitored through $\ce{^{17}O}$ NMR spectroscopy in the most extremely acidic condensed phase superacid we can make, fluoroantimonic acid ($\ce{HF:SbF5}$ or $\ce{HSbF6}$). It seems that even the slightly weaker but still very much superacidic magic acid $\ce{HSO3F:SbF5}$ is not strong enough to effect measurable protonation of $\ce{H3O+}$ into $\ce{H4O^{2+}}$. It likely also can exist in the gas phase by exposing water to bare protons, and might have some importance in astrochemistry. Relatedly, $\ce{H4S^{2+}}$ also has been inferred to exist through the same type of measurements, and is easier to make, existing in magic acid mixtures.
A nice source for your superacidic needs is books by George Olah, the father of superacidic chemistry. In particular, Onium Ions has a section on the protohydronium dication $\ce{H4O^{2+}}$ on page 435. There are many other curious cations analyzed such as $\ce{CH6^{2+}}$ and even $\ce{CH7^{3+}}$. When it comes to superacids, nothing is sacred!
