A kit for modular assembly of a piece of furniture “in situ” that comprises lower, intermediate, and upper main support members. Each of the main support members includes insertion slots with chamfered edges that are oriented at different angles in the periphery. The lower main support member has first and second foot slots that include locking ends. A plurality of cantilevered members having open insertion slots with chamfered edges each have a front fit-in section and a rear insertion section that end in an insertion stop. The open insertion slots are disposed in the periphery of the cantilevered members so that they may engage the oriented insertion slots. The first and second foot members are configured to engage first and second foot slots. The main support members have mutual engagement means that include coupling members and fastening openings for structural assembly of a piece of furniture.