This work considers the problem of dynamic power allocation in the downlink of multi-cell networks, where each cell utilizes non-orthogonal multiple access (NOMA)-based resource allocation. Also, coordinated multi-point (CoMP) transmission is utilized among multiple cells to serve users experiencing severe inter-cell interference (ICI). More specifically, we consider a two-tier heterogeneous network (HetNet) consisting of a high-power macro cell underlaid with multiple low-power small cells each of which uses the same resource block. Under this {\em CoMP-NOMA framework}, CoMP transmission is applied to a user experiencing high channel gain with multiple base stations (BSs)/cells, while NOMA is utilized to schedule CoMP and non-CoMP users over the same transmission resources, i.e., time, spectrum and space. Different CoMP-NOMA models are discussed, but focus is primarily on the joint transmission CoMP-NOMA (JT-CoMP-NOMA) model. For the JT-CoMP-NOMA model, an optimal joint power allocation problem is formulated and the solution is derived for each CoMP-set consisting of multiple cooperating BSs (i.e., CoMP BSs). To overcome the substantial computational complexity of the joint power optimization approach, we propose a distributed power optimization problem at each cooperating BS whose optimal solution is independent of the solution of other coordinating BSs. The validity of the distributed solution for the joint power optimization problem is provided and numerical performance evaluation is carried out for the proposed CoMP-NOMA models including JT-CoMP-NOMA and coordinated scheduling CoMP-NOMA (CS-CoMP-NOMA). The obtained results reveal significant gains in spectral and energy efficiency in comparison with conventional CoMP-orthogonal multiple access (CoMP-OMA) systems.