Recent research has introduced the notion of an Intelligent Reflective Surface (IRS) so as to boost the source–destination communication environment. IRS refers to a plane that consists of a number of passive elements that have a smaller size than the wavelength of the incident signal. Those elements use reflection to beam-form and to forward the incident radio signals toward the intended destination without power consumption. This article examines the performance of an IRS-based non-orthogonal multiple access (NOMA) system, and adopts the idea of using multiple IRS planes. It additionally investigates improving the performance of an IRS-NOMA combination through proposing various solutions that include optimizing the overall number of the IRS elements as a first step. After that, a closed form expression is derived for the considered IRS-NOMA system to determine the optimal number of the reflective elements. Secondly, the paper utilizes a new approach termed as multiple-IRS-based NOMA. This encompasses using multiple reflective planes (multi-IRS) along with IRS-NOMA, to boost the received signal characteristics, especially in situations where it is there a weak or no direct link between the source and the destination. An energy efficiency-spectral efficiency (EE-SE) trade-off is likewise presented, so as to have a complete view of the IRS-NOMA performance, along with the proposed solutions. The obtained simulation results depicts that IRS-NOMA is better than the existing orthogonal techniques. In addition, the results confirm that exploiting multiple IRSs offers a considerable gain in performance, as it enhances the conditions of the propagation environment. In specific, the considered case of a two IRS surfaces-assisted NOMA system offers higher performance levels than the case of a single IRS surface-assisted NOMA system.