A method and apparatus are provided for holding and positioning objects for a single diamond point turning operation. The objects which may include liquid phase epitaxy films are mounted on multiple platforms (10, 46). The platforms (10, 46) are securely connected to a base (20). The platforms (10, 46) are positioned, independently from one another, for elevation and orientation relative to the base (20) while the platforms (10, 46) are securely connected to the base (20).