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We derive the capacity region of arbitrarily varying multiple-access channels (AV-MACs) with conferencing encoders for both deterministic and random coding. For a complete description, it is sufficient that one conferencing capacity is positive. We obtain a dichotomy: either the channel's deterministic capacity region is zero or it equals the 2-D random coding region. We determine exactly when either case holds. We also discuss the benefits of conferencing. We give the example of an AV-MAC which does not achieve any nonzero rate pair without encoder cooperation, but the 2-D random coding capacity region if conferencing is possible. Unlike compound multiple-access channels, arbitrarily varying multiple-access channels may exhibit a discontinuous increase of the capacity region when conferencing in at least one direction is enabled.