Capacity limitations of perceptual surface completion were assessed using a simultaneous-sequential method. Observers searched among multiple surfaces requiring perceptual completion in front of other objects (modal completion) or behind other objects (amodal completion). In the simultaneous condition, all surfaces were presented at once, whereas in the sequential condition, they appeared in subsets of 2 at a time. For both modal and amodal surface completion, performance was as good in the simultaneous condition as in the sequential condition, indicating that surface completion unfolds independently for multiple surfaces across the visual field (i.e., has unlimited capacity). We confirmed this was due to the formation of surfaces defined by the pacmen inducers, and not simply to the detection of individual features of the pacmen inducers. These results provide evidence that surface-completion processes can be engaged and unfold independently for multiple surfaces across the visual field. In other words, surface completion can occur through unlimited-capacity processes. These results contribute to a developing understanding of capacity limitations in perceptual processing more generally.