This paper studies the throughput maximization of a dense multiple access network of low-rate subscribers that share the same practical Forward Error Correction (FEC) code and modulation scheme, and transmit to a central node that implements a Successive Soft Interference Cancellation (soft SIC) strategy in order to mitigate Multiple Access Interference (MAI). In the user-asymptotic case, we make use of Variational Calculus (VC) tools to derive, in terms of the Packet Error Rate (PER) of the shared encoder and the Residual Energy (RE) from imperfect cancellation, the optimum energy profile that maximizes the network spectral efficiency, when a sum power constraint at the SIC input is enforced. Comparative performance analyses using a representative encoder are carried out. Simulation results show the benefit of the adopted soft SIC scheme in front of other SIC strategies, obtaining relevant throughput gains under high traffic loads.