Reciprocal structures or nexorade are composed by the assembling of groups of three or more beams mutually connected by mono-lateral T joints in a way that any relative movement is suppressed. This kind of structures can be easily built in relatively unprepared sites, dismantled, transported and re-used even by not specialized handcraft. For these reasons, reciprocal structures have been widely used in the past for military purposes, and nowadays they seem to satisfy very well the different requirements of a quick and temporary shelter of a large archaeological area when they are shaped as grid shells. This paper proposes the design of a reversible, reciprocal framed grid shell to shelter the archaeological site of the Roman Shipwrecks in Pisa. The structure must protect excavations and archaeologists from the weather and provide an easy access to visitors. Additionally, it must allow for easy disassembling and moving to another site. The design choices aim at optimizing both structural efficiency and esthetical qualities. A parametric workflow for both the form finding and the digital fabrication processes has been developed, and a prototype of accommodative steel T-joint for timber reciprocal beams has been realized. Finally, a model using CNC-cutting tested the structural feasibility of such a design approach.