Possibilities for behavior (i.e., affordances) can be perceived with units spanning anatomical components and external objects. For example, affordances for standing on an inclined surface can be perceived with an object held in the hand or attached to the head. We investigated whether these two person-plus-object perceptual systems exhibit the same pattern of nonlinear phase transitions in perception of this affordance. Blindfolded participants explored an inclined surface with a rod held in the hand or attached to the head and reported whether they could stand on that surface. Inclinations were presented in ascending or descending sequences. In both conditions, responses exhibited negative hysteresis – perceptual boundaries occurred at steeper angles for descending than for ascending sequences. The generalization of this pattern across components that differ in physiology, sensitivity, and experience is consistent with both the soft assembly of perceptual devices and with a dynamical systems perspective on perception of affordances.