We present a new generation of piezoresistive nanomechanical Membrane-type Surface stress Sensor (MSS) chips, which consist of a two dimensional array of MSS on a single chip. The implementation of several optimization techniques in the design and microfabrication improved the piezoresistive sensitivity by 3~4 times compared to the first generation MSS chip, resulting in a sensitivity about ~100 times better than a standard cantilever-type sensor and a few times better than optical read-out methods in terms of experimental signal-to-noise ratio. Since the integrated piezoresistive read-out of the MSS can meet practical requirements, such as compactness and not requiring bulky and expensive peripheral devices, the MSS is a promising transducer for nanomechanical sensing in the rapidly growing application fields in medicine, biology, security, and the environment. Specifically, its system compactness due to the integrated piezoresistive sensing makes the MSS concept attractive for the instruments used in mobile applications. In addition, the MSS can operate in opaque liquids, such as blood, where optical read-out techniques cannot be applied.