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PercepNet, a recent extension of the RNNoise, an efficient, high-quality and real-time full-band speech enhancement technique, has shown promising performance in various public deep noise suppression tasks. This paper proposes a new approach, named PercepNet+, to further extend the PercepNet with four significant improvements. First, we introduce a phase-aware structure to leverage the phase information into PercepNet, by adding the complex features and complex subband gains as the deep network input and output respectively. Then, a signal-to-noise ratio (SNR) estimator and an SNR switched post-processing are specially designed to alleviate the over attenuation (OA) that appears in high SNR conditions of the original PercepNet. Moreover, the GRU layer is replaced by TF-GRU to model both temporal and frequency dependencies. Finally, we propose to integrate the loss of complex subband gain, SNR, pitch filtering strength, and an OA loss in a multi-objective learning manner to further improve the speech enhancement performance. Experimental results show that, the proposed PercepNet+ outperforms the original PercepNet significantly in terms of both PESQ and STOI, without increasing the model size too much.