I am oxidizing KI in aqueous medium, and expect the formation of triiodide ion in the solution. I do expect the oxidation of triiodide ion, as I am observing complex kinetics.
Triodoide is formed by combining aqueous solution of iodide salt (e.g.KI) and iodine as this equation shows : I− + I2 ⇌ I−3 . Iodine acts as oxidizing agent but is not a strong one compared to other members of the halogen family above it in the periodic table.
The triiodide ion cannot protonate other species but it can get protonated with the protonated polyiodide complex I2H+ being the dominant product, as far as I know.
You should also expect some other polyiodides to form. Catenation with iodine does not end with I3-. Consult for example Greenwood and Earnshaw, Chemistry of the Elements, 1998.