Various types of target information have been considered in aspect-based sentiment analysis, such as entities and aspects. Existing research has realized the importance of targets and developed methods with the goal of precisely modeling their contexts via generating target-specific representations. However, all these methods ignore that these representations cannot be learned well due to the lack of sufficient human-annotated target-related reviews, which leads to the data sparsity challenge, a.k.a. cold-start problem here. In this paper, we focus on a more general multiple entity aspect-based sentiment analysis (ME-ABSA) task which aims at identifying the sentiment polarity of different aspects of multiple entities in their context. Faced with severe cold-start scenario, we develop a novel and extensible deep memory network framework with cold-start aware computational layers which use frequency-guided attention mechanism to accentuate on the most related targets, and then compose their representations into a complementary vector for enhancing the representations of cold-start entities and aspects. To verify the effectiveness of the framework, we instantiate it with a concrete context encoding method and then apply the model to the ME-ABSA task. Experimental results conducted on two public datasets demonstrate that the proposed approach outperforms state-of-the-art baselines on ME-ABSA task.