This study looks at two treatments, extracorporeal photopheresis (ECP) and mogamulizumab, for a rare skin cancer called erythrodermic cutaneous T cell lymphoma (CTCL). CTCL starts in white blood cells (T cells) and causes red skin rashes. ECP is a procedure where blood is taken out, treated with UV light, and returned to the body. Mogamulizumab is a special medicine that stops cancer cells from growing and spreading. The study will see how well these treatments work together to kill cancer cells and improve the immune system's response.

• Participants will receive treatment over 28-day cycles for up to 6 cycles, with potential for more if showing good response.
• The study involves regular medical visits and blood tests to monitor progress and side effects.
• Participants cannot have had prior treatment with mogamulizumab and must follow specific health guidelines to qualify.

After treatment, patients will be monitored regularly for up to a year to check on their health and any cancer changes.