Although the multistage interference cancellation detector is simple in structure, its performance degrades when the number of active users becomes large. In some cases, the performance is even worse than that without cancellation, due to the lack of the exact knowledge of the interfering signal in cancellation. Partial interference cancellation suggested by Divsalar and Simon (see IEEE Trans. Commun., vol.46, p.258-68, 1998) tries to remedy this weakness by reducing the cost of a wrong interference estimation through a weight in each stage. This paper presents an adaptive multistage structure based on the partial interference cancellation approach. In this structure, the weights are obtained by minimizing the mean-square error between the received signal and its estimate through a least mean square (LMS) algorithm. The resulting weights contain reliability information for the hard decisions made in the previous stage. Neither a training sequence nor a pilot signal is needed in the proposed scheme, and its complexity is much lower than that of linear multiuser detectors. Simulation results show that the proposed scheme can outperform some of the existing interference cancellation methods in both the additive white Gaussian noise (AWGN) and the multipath fading channels.