This is an open-label, non-controlled trial of standard medical care plus the TORAYMYXIN PMX-20R (PMX cartridge), in subjects with endotoxemia and septic shock. Subjects in ICUs will be assessed for septic shock using known or suspected infection and hypotension requiring vasopressor support as primary criteria. Endotoxemia will be assessed using the Endotoxin Activity Assay. Consented eligible subjects will receive two interventions with the PMX cartridge approximately 24 hours apart.The status of all subjects will be followed for 28 days, and long term follow-ups completed at 3 months, 6 months and 12 months.