The potential role of positive interactions among co-invaders is at the core of the invasional meltdown hypothesis. The interaction of non-native species could result in an exacerbation of each other’s effects. Thus, the resulting effect of multiple non-native species on ecosystems can be greater than the sum of their individual effects. We designed an analytical framework and a set of mesocosm experiments to assess the potential synergistic effects of three non-native species (Limnoperna fortunei, Astronotus crassipinnis, and Hydrilla verticillata) in a highly invaded floodplain in southern Brazil. We analyzed ecosystem, community, and population attributes in scenarios with non-natives. Our hypothesis of a synergistic effect was not supported. Even though effects of the invasive species were detected for all ecological levels, evidence indicated that these effects were additive. In addition to adding to the statement that origin (i.e., native vs. non-native status) does matter, we provide a tool to differentiate additive, synergistic, and antagonistic effects in situations with multiple invasions, and experimentally demonstrate additive effects of non-native species at different ecological levels.