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Arbitrary amplitude ion-acoustic supersolitons are investigated with two-temperature superthermal electrons in an unmagnetized negative ion plasma. In this study, we have considered the plasma containing two cold ion species with different masses, ion concentration and charge multiplicity, and two superthermal (non-Maxwellian) electrons. The energy integral equation has been derived by using the Sagdeev pseudopotential technique. We have investigated that both negative and positive potential supersolitons and solitons can exist in the selected domain of Mach number. A numerical analysis shows that the ion-acoustic supersolitons appear below the acoustic speed (M s) . The amplitude of the supersoliton is found larger than the soliton. The formation of solitons and supersolitons (both polarity) is analyzed by phase portrait of the dynamic of the plasma system. The plasma system also supports the coexistence of compressive and rarefactive solitons for a particular set of plasma parameters. The present study is focused on ion-acoustic solitary and supersolitary waves in the D-and F-regime of Earth's ionosphere and experimentally produced plasmas (Ar+, F−) and (Ar+, SF−6) ion species. The present investigation may be helpful in understanding the nonlinear behavior of supersoliton and soliton in space and laboratory plasmas, where negative ions are present with superthermal electrons at two temperatures. [ABSTRACT FROM AUTHOR]