Self-attention models have achieved the state-of-the-art performance in sequential recommender systems by capturing the sequential dependencies among user–item interactions. However, they rely on adding positional embeddings to the item sequence to retain the sequential information, which may break the semantics of item embeddings due to the heterogeneity between these two types of embeddings. In addition, most existing works assume that such dependencies exist solely in the item embeddings, but neglect their existence among the item features. In our previous study, we proposed a novel sequential recommendation model, i.e., MLP4Rec, based on the recent advances of MLP-Mixer architectures, which is naturally sensitive to the order of items in a sequence because matrix elements related to different positions of a sequence will be given different weights in training. We developed a tri-directional fusion scheme to coherently capture sequential, cross-channel, and cross-feature correlations with linear computational complexity as well as much fewer model parameters than existing self-attention methods. However, the cascading mixer structure, the large number of normalization layers between different mixer layers, and the noise generated by these operations limit the efficiency of information extraction and the effectiveness of MLP4Rec. In this extended version, we propose a novel framework – SMLP4Rec for sequential recommendation to address the aforementioned issues. The new framework changes the flawed cascading structure to a parallel mode, and integrates normalization layers to minimize their impact on the model’s efficiency while maximizing their effectiveness. As a result, the training speed and prediction accuracy of SMLP4Rec are vastly improved in comparison to MLP4Rec. Extensive experimental results demonstrate that the proposed method is significantly superior to the state-of-the-art approaches. The implementation code is available online to ease reproducibility.