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We examine the fluid phase behaviour of the binary mixture of hard superellipses using the scaled particle theory The superellipse is a general two dimensional convex object which can be tuned between circular and rectangular shapes continuously at a given aspect ratio. We find that the shape of the particle affects strongly the stability of isotropic nematic and tetratic phases even if the aspect ratios of both species are fixed. While the isotropic isotropic demixing transition can be ruled out using the scaled particle theory the first order isotropic nematic and the nematic nematic demixing transition can be stabilized with strong fractionation between the components. It is observed that the demixing tendency is strongest in small rectangle large ellipse mixtures. Interestingly, it is possible to stabilize the tetratic order at lower densities in the mixture of hard squares and rectangles where the long rectangles form nematic phase, while the squares stay in tetratic order.