In case of austenitic stainless steel alloying element stabilise austenite by increasing the austenitic area in iron carbon diagram by decreasing eutectoid composition and decreasing the eutectoid temperature
If we Have for example Titanium metal ... we will find that highly pure titanium is a relatively ductile material whose mechanical properties are not suitable for the manufacture of parts to be subjected to high stresses. At room temperature, titanium has a close-packed hexagonal structure (called a-phase) which undergoes a crystal transformation at about 882°C into a body-centred cubic structure (called ~-phase) which remains stable up to the melting point, at 1660°C. a-phase alloys are weldable and ductile, but unable to undergo
any heat treatment, while ~-phase alloys prove hard and brittle. The introduction of aluminium enlarges the field of existence of the a-phase and thereby determines an increase in the a-~ transition temperature, stabilizing the a-phase at room temperature and consequently increasing its hotworkability. the same thing when vanadium addition ... you can imagine why element stabilizes particular phases.