The improvement of MRI speed with parallel acquisition is ultimately an SNR-limited process. To offset acquisition- and reconstruction-related SNR losses, practical parallel imaging at high accelerations should include the use of a many-element array with a high intrinsic signal-to-noise ratio (SNR) and spatial-encoding capability, and an advantageous imaging paradigm. We present a 32-element receive-coil array and a volumetric paradigm that address the SNR challenge at high accelerations by maximally exploiting multidimensional acceleration in conjunction with noise averaging. Geometric details beyond an initial design concept for the array were determined with the guidance of simulations. Imaging with the support of 32-channel data acquisition systems produced in vivo results with up to 16-fold acceleration, including images from rapid abdominal and MRA studies.