A bearing support assembly includes a squirrel cage defining a longitudinal axis and having a cylindrical portion defining a bearing seat. The squirrel cage is configured and adapted to provide a first level of radial support stiffness between a housing and a bearing seated in the bearing seat. A damper sleeve is operatively coupled to the cylindrical portion of the squirrel cage through a fluid film to dampen relative radial motion between the damper sleeve and the squirrel cage. A radial spring component is operatively connected to a side of the damper sleeve radially opposite the cylindrical portion of the squirrel cage to provide a second level of radial support stiffness.