Speech emotion recognition (SER) aims to automatically recognize emotional category for a given speech utterance. The performance of a SER system heavily relies on the effectiveness of global representation expressed at utterance level. To effectively extract such a global feature, the mainstream of recent SER architectures adopts a pipeline with two key modules, feature extraction and aggregation. Although variant module designs have brought impressive progresses, SER is still a challenging task. In contrast with those previous works, herein we propose a novel strategy for global SER feature extraction by applying an additional enhancement module on top of the current SER pipeline. To verify its effect, an end-to-end SER architecture is proposed where stacked multiple transformer layers are explored to enhance the aggregated global feature. Such an architecture is evaluated on IEMO-CAP and results strongly substantiate the effectiveness of our proposal. In terms of weighted accuracy on four emotion categories, our proposed SER system outperforms the prior arts by a large margin of relatively 20% improvement. Our codes and the pre-trained SER models are made publicly available.