It has been shown that a CDMA fading channel followed by a generic multiuser detection front end essentially decouples into a bank of Gaussian single-user channels in the large-system limit. This paper extends the decoupling result to multicarrier (MC) CDMA and multirate CDMA. In MC-CDMA, frequency-selective fading and equal-rate users are considered. In multirate CDMA, flat fading is assumed, while users may employ a combination of adaptive modulation, variable spreading factor, and multicode schemes to support different data rates. Using statistical physics techniques, it is found that the decoupling principle still holds in both scenarios, i.e., each user experiences an equivalent single-user Gaussian channel, where the degradation in the SNR, known as the multiuser efficiency, is obtained analytically by solving a set of joint equations. The results apply to optimal multiuser detectors as well as many well-know suboptimal detectors.