The complex nature of single organ failure potentially leading to multiple organ dysfunction syndrome (MODS) in critically ill patients necessitates integrated supportive therapy. Rather than a primary disease, acute kidney injury (AKI) is considered a window to a potentially serious underlying systemic disease, which may partially explain the high morbidity and mortality rates associated with the condition. Renal replacement therapy (RRT) has been routinely used for more than a decade in various intensive care settings and there has also been an increase in the use of extracorporeal membrane oxygenation and extracorporeal carbon dioxide removal. When these renal and cardiopulmonary modalities are used together, a multidisciplinary approach is necessary to minimize negative interactions and unwanted adverse effects. In this review, we describe the patterns of organ crosstalk between the native and artificial organs, the incidence of AKI and need for RRT and associated mortality after extracorporeal organ support (ECOS) therapy, including the potential short- and long-term advantages and disadvantages of organ support in terms of renal function. We also review potential indications of RRT outside its conventional indications in patients with MODS, as well as technical considerations when RRT is used alongside other organ support therapies. Overall, available literature has not definitely established the ideal timing of these interventions, and whether early implementation impacts organ recovery and optimizes resource utilization is still a matter of open debate: it is possible that future research will be devoted to identify patient groups that may benefit from short- and long-term multiple organ support.