Sequential recommendation systems have become a research hotpot recently to suggest users with the next item of interest (to interact with). However, existing approaches suffer from two limitations: (1) The representation of an item is relatively static and fixed for all users. We argue that even a same item should be represented distinctively with respect to different users and time steps. (2) The generation of a prediction for a user over an item is computed in a single scale (e.g., by their inner product), ignoring the nature of multi-scale user preferences. To resolve these issues, in this paper we propose two enhancing building blocks for sequential recommendation. Specifically, we devise a Dynamic Item Block (DIB) to learn dynamic item representation by aggregating the embeddings of those who rated the same item before that time step. Then, we come up with a Prediction Enhancing Block (PEB) to project user representation into multiple scales, based on which many predictions can be made and attentively aggregated for enhanced learning. Each prediction is generated by a softmax over a sampled itemset rather than the whole item space for efficiency. We conduct a series of experiments on four real datasets, and show that even a basic model can be greatly enhanced with the involvement of DIB and PEB in terms of ranking accuracy. The code and datasets can be obtained from https://github.com/ouououououou/DIB-PEB-Sequential-RS