A multi-ratio gearbox housing for a vehicle is made of light metal material and includes a first bearing seat having a cylindrical inner surface, and a reinforcement member having a first cylindrical inner surface surrounding the first bearing seat for reducing thermal radial expansion of the first bearing seat, the reinforcement member being of a material the coefficient of thermal expansion of which is less than the coefficient of thermal expansion of the light metal material of the housing. The reinforcing member is a cast-in insert arranged in the housing, and a radial distance between the first cylindrical inner surface and the cylindrical inner surface of the first bearing seat is substantially constant along circumferential lines of the first bearing seat, facilitating improved form stability of the cylindrical inner surface of the first bearing seat over the temperature operating range of the housing.