This study uses the classical density functional theory (DFT) of freezing to investigate phase transitions in ellipsoidal-spherical binary mixtures interacting via a generalised Gay-Berne (GB) intermolecular potential, with a focus on I-N, I-SmA and N-SmA transitions. The mixtures, consisting mainly of ellipsoids, contain spherical additives at concentrations of 5%, 10% and 15%. The pair correlation functions, which are crucial for the DFT, are derived from Percus-Yevick integral equation theory. Our results show a significant influence of spherical additives on liquid crystalline phases formed by ellipsoids. At an ellipsoid length-to-width ratio of 3.0, only the I-N transition is observed, with the SmA phase remaining unstable under all conditions. Increasing the ellipsoidal length-to-width ratio to 𝜅 = 4.0 introduces the SmA phase, whose stability depends on the concentration and size of the spherical additives. The stability of the SmA phase decreases with increasing concentration and size of the spheres. Phase diagrams, which are shown in temperature-density and pressure-temperature planes, emphasise the influence of the size of the spherical dopants on the phase stability.