A multi-level interposer plate and a multi-chip module (MCM) that includes the multi-level interposer plate are described. First surfaces and second surfaces in different regions of the multi-level interposer plate have associated, different thicknesses. Moreover, first micro-spring connectors and second micro-spring connectors are respectively disposed on the first surfaces and the second surfaces. In the MCM, a given one of the first surfaces of the multi-level interposer plate faces a bridge chip in a first layer in an array of chips in the MCM so that first connectors, disposed on the bridge chip, mechanically and electrically couple to the first micro-spring connectors. Similarly, a given one of the second surfaces of the multi-level interposer plate faces an island chip in a second layer in the array of chips so that second connectors, disposed on the island chip, mechanically and electrically couple to the second micro-spring connectors.