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We consider the multiple access source coding (MASC) problem (also known as the Slepian-Wolf problem) for situations where the joint source statistics are unknown a priori. Since neither encoder receives information about the joint source statistics, we allow an asymptotically negligible amount of communication between the encoders. We prove the existence of universal 2-encoder linked MASCs (LMASCs) with rates approaching the Slepian-Wolf bound, demonstrate the tightness of this bound, and calculate the rate of convergence of the proposed universal LMASC. The result generalizes to M>2 encoders. We also consider scenarios where the number of bits passed between the system encoders is allowed to grow linearly in the code dimension; in these scenarios one encoder can act as a conduit for the flow of another encoder's information.