By flexibly manipulating the radio propagation environment, reconfigurable intelligent surface (RIS) is a promising technique for future wireless communications. However, the single-side coverage and double-fading attenuation faced by conventional RISs largely restrict their applications. To address this issue, we propose a novel concept of multi-functional RIS (MF-RIS), which provides reflection, transmission, and amplification simultaneously for the incident signal. With the aim of enhancing the performance of a non-orthogonal multiple-access (NOMA) downlink multiuser network, we deploy an MF-RIS to maximize the sum rate by jointly optimizing the active beamforming and MF-RIS coefficients. Then, an alternating optimization algorithm is proposed to solve the formulated non-convex problem by exploiting successive convex approximation and penalty-based method. Numerical results show that the proposed MF-RIS outperforms conventional RISs under different settings.