To reduce multiuser interference and maximize the spectrum efficiency in orthogonal frequency division duplexing massive multiple-input multiple-output (MIMO) systems, the downlink channel state information (CSI) estimated at the user equipment (UE) is required at the base station (BS). This paper presents a novel method for massive MIMO CSI feedback via a one-sided one-for-all deep learning framework. The CSI is compressed via linear projections at the UE, and is recovered at the BS using deep learning (DL) with plug-and-play priors (PPP). Instead of using handcrafted regularizers for the wireless channel responses, the proposed approach, namely CSI-PPPNet, exploits a DL based denoisor in place of the proximal operator of the prior in an alternating optimization scheme. In this way, a DL model trained once for denoising can be repurposed for CSI recovery tasks with arbitrary compression ratio. The one-sided one-for-all framework reduces model storage space, relieves the burden of joint model training and model delivery, and could be applied at UEs with limited device memories and computation power. Extensive experiments over the open indoor and urban macro scenarios show the effectiveness and advantages of the proposed method.