Session-based recommender systems (SBRSs) have become extremely popular in view of the core capability of capturing short-term and dynamic user preferences. However, most SBRSs primarily maximize recommendation accuracy but ignore user minor preferences, thus leading to filter bubbles in the long run. Only a handful of works, being devoted to improving diversity, depend on unique model designs and calibrated loss functions, which cannot be easily adapted to existing accuracy-oriented SBRSs. It is thus worthwhile to come up with a simple yet effective design that can be used as a plugin to facilitate existing SBRSs on generating a more diversified list in the meantime preserving the recommendation accuracy. In this case, we propose an end-to-end framework applied for every existing representative (accuracy-oriented) SBRS, called diversified category-aware attentive SBRS (DCA-SBRS), to boost the performance on recommendation diversity. It consists of two novel designs: a model-agnostic diversity-oriented loss function, and a non-invasive category-aware attention mechanism. Extensive experiments on three datasets showcase that our framework helps existing SBRSs achieve extraordinary performance in terms of recommendation diversity and comprehensive performance, without significantly deteriorating recommendation accuracy compared to state-of-the-art accuracy-oriented SBRSs.