The future will be marked by a highly intelligent, automated, and ubiquitous digital world, requiring fast and reliable connectivity across physical, digital, and biological realms. While Multi-access Edge Computing (MEC) has facilitated swift connectivity between mobile devices and resource-rich cloud servers, current state-of-the-art solutions may struggle to meet the demands of compute-and bandwidth-intensive applications in the envisioned digital society. To make up for the capacity, 5G and the upcoming 6G expand the channel bandwidth, exacerbating spectrum scarcity and increasing network costs. To enhance Quality of Service (QoS) and minimize expenses, a recent proposal suggests parallel offloading using multiple radio access technologies (RATs) available on mobile devices, such as Wi-Fi Direct, Wi-Fi, and 5G. However, these technologies differ in performance, including throughput, delay, and response to physical conditions. Inappropriate marshalling of RATs can lead to issues like out-of-sequence packets, resource wastage, and reduced throughput, resulting in longer service delays. To address this problem, we evaluate RAT performance and develop a convex Continuous Non-Linear Program (CNLP) to optimally utilize their capacities, ensuring load distribution aligns with their performance. Additionally, we optimize capacity distribution at relay nodes to ensure smooth MEC data transfer based on incoming load. Numerical results demonstrate significant improvements in terms of throughput, delay, and QoS compared to other techniques involving multiple RATs for computation offloading.