This paper proposes a nonparametric bias-reduction regression estimator which can accommodate two empirically relevant data environments. The first data environment assumes that at least one of the predictor variables is discrete. In such an empirical framework, a "cell" approach, which consists of estimating a separate regression for each discrete cell has generally been employed. However, the "cell" estimator may be inefficient in that it does not include data from the other cells when estimating the regression function for a given cell. The second data environment assumes that the researcher is faced with a system of regression functions that belong to different experimental units. In each case, the new estimator attempts to reduce estimation error by incorporating extraneous data from the remaining experimental units (or cells) when estimating a given individual regression function. Consistency of the proposed estimator is established and Monte Carlo simulations demonstrate its strong finite sample performance.