This paper introduces a two-dimensional (2-D) processing approach for the analysis of multi-pitch speech sounds. Our framework invokes the short-space 2-D Fourier transform magnitude of a narrowband spectrogram, mapping harmonically related signal components to multiple concentrated entities in a new 2-D space. First, localized time-frequency regions of the spectrogram are analyzed to extract pitch candidates. These candidates are then combined across multiple regions for obtaining separate pitch estimates of each speech-signal component at a single point in time. We refer to this as multi-region analysis (MRA). By explicitly accounting for pitch dynamics within localized time segments, this separability is distinct from that which can be obtained using short-time autocorrelation methods typically employed in state-of-the-art multi-pitch tracking algorithms. We illustrate the feasibility of MRA for multi-pitch estimation on mixtures of synthetic and real speech.