In the computer program MGROUP used by ETS for fitting the latent regression model to data from NAEP and other programs, the integration is currently done either by numerical quadrature for problems up to two dimensions or by an approximation of the integral. CGROUP, the current operational version of the MGROUP program used in NAEP and other assessments since 1993, is based on Laplace approximation, which may not provide fully satisfactory results, especially if the number of items per scale is small (see, e.g., Thomas, 1993a, or von Davier & Sinharay, 2004). There is scope for improvement in the technique used. This paper extends the NAEP BGROUP program to higher dimensions. Two real data analyses, one with a medium-sized data set and another with a large data set, show that the extension promises to be useful for fitting the NAEP model.