Traditional speech enhancement systems produce speech with compromised quality. Here we propose to use the high quality speech generation capability of neural vocoders for better quality speech enhancement. We term this parametric resynthesis (PR). In previous work, we showed that PR systems generate high quality speech for a single speaker using two neural vocoders, WaveNet and WaveGlow. Both these vocoders are traditionally speaker dependent. Here we first show that when trained on data from enough speakers, these vocoders can generate speech from unseen speakers, both male and female, with similar quality as seen speakers in training. Next using these two vocoders and a new vocoder LPCNet, we evaluate the noise reduction quality of PR on unseen speakers and show that objective signal and overall quality is higher than the state-of-the-art speech enhancement systems Wave-U-Net, Wavenet-denoise, and SEGAN. Moreover, in subjective quality, multiple-speaker PR out-performs the oracle Wiener mask.