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Recent studies have found successive interference cancellation (SIC) schemes employing blind source separation (BSS) methods to be promising competitors for conventional IC schemes. The main reason for this is the inherent ability of BSS to mitigate many kinds of interference sources e.g. multiaccess, multipath and out-of-cell interferences. We propose a modification of a BSS-SIC -type receiver and high-light its nice property of being able to drastically enhance the number of users a system can support, given a certain bit-error-rate requirement, compared to that of conventional parallel and successive interference cancellation (PIC and SIC, respectively) and BSS-alone schemes. The paper also shows how the proposed scheme relaxes the inherent weakness of standard BSS. Namely, the inadequate-ness in highly loaded systems due to the "more sources than observations"-problem, which can be somewhat circumvented in BSS-SIC -type receivers.