In non-orthogonal multiple access (NOMA), user pairing, power allocation, and performance evaluation are typically performed while assuming that all users have equal symbol rates. However, such an assumption may significantly limit the design flexibility of NOMA and devalue its potential. Therefore, this paper considers a generalized scenario where the user-paring process may include users with different symbol rates, and thus, the proposed configuration is denoted as multi-rate NOMA (MRNOMA). In MR-NOMA, the relation between the symbol rate and energy is exploited to add a new degree of freedom when assigning power to the paired users. That is, the fact that the symbol energy is proportional to the symbol duration extends the range of power values that can be allocated to the high symbol rate user while satisfying the quality-of-service requirements for all users. Consequently, the number of served users can be increased, or such a feature can be used to increase the link throughput. The obtained results show that with optimal power selection, both the high and low symbol rate users can achieve lower bit error rates (BERs), which in turn increases the system throughput as a result of the improved transmission reliability.