Curvilinear coordinate Monte Carlo phase space integration and a series of full-dimensional fitted potential energy surfaces are used to study the effectiveness of reduced-dimensional models for predicting rovibrational anharmonicity at high temperatures. Fully coupled and fully anharmonic, but classical, rovibrational partition functions Q are computed for 14 species with two or three fluxional modes (inversions or torsions) and as many as 30 degrees of freedom. These results are converted to semiclassical anharmonicity correction factors f and are analyzed alongside results obtained previously for 22 species with up to two fluxional modes. As expected, fluxional species show considerable variation in f at high temperatures; f is as small as 0.2 for acetone and is as large as 9 for methylene glycol at 2500 K. This set of full-dimensional results is used to test the accuracy of reduced-dimensional models where fluxional modes are treated as coupled to one another but as separable from the remaining nonfluxional modes. For most systems, we find that such an approximation is accurate at high temperatures, with average errors in Q of just similar to 25%. For some systems, however, larger errors are found, and these are attributed to strong coupling of the fluxional modes to one or more nonfluxional modes. In particular, we identify strong coupling to low-frequency bends for some systems, and we show that by comparing curvilinear and rectilinear harmonic frequencies for the fluxional modes, we can estimate the effect of this coupling on rovibrational anharmonicity. We also quantify the accuracy of the more severe but common assumption of treating fluxional modes as separable from one another, that is, as sets of uncoupled one-dimensional inversions and torsions. This approach can work well for methyl and alkyl rotors, but it is shown to have errors as large as a factor of 7 at high temperatures for more complex systems. Finally, we note that while the present analysis focuses on the treatment of fluxional modes, the collective anharmonicity correction associated with the more numerous nonfluxional modes, although simpler to describe, comprises a significant fraction of the overall anharmonicity.