Provided are methods and apparatuses for processing objects by applying different forces and/or pressure levels to different portions of surfaces of these objects. An apparatus may include a flexible wall and a contact member. In some embodiments, the flexible wall forms a bladder such that the contact member is disposed inside the bladder. During operation, the flexible wall may be pressed against an object using a pressure differential across the wall (e.g., by pressurizing the bladder). This creates a first force acting on a first portion of the object surface. Furthermore, the contact member may be forced against the flexible wall and apply a second force to a second portion of the object surface through the wall. The second portion of the object surface may be a subset of the first portion or an entirely different portion.