Multiple Myeloma is a type of blood cancer in cells made in the bone marrow. Relapsed means the previous cancer treatment worked for a while but stopped working, over time. Refractory means people did not respond to previous cancer treatment. TAK-169 is a medicine that binds to the surface of multiple myeloma cells called CD38 cells. It delivers a dose of chemotherapy to the CD38 cells. This study is in 2 parts. The main aims of Part 1 of the study are to check how much TAK-169 a person can receive without getting side effects from it, and to work out the best dose of TAK-169 to give people to treat their cancer. The main aim of Part 2 of the study is to learn if the condition of people with multiple myeloma improves after treatment with TAK-169. Another aim is to check for side effects from TAK-169. In Part 1, at the first visit, the study doctor will check who can take part. Participants who can take part will receive TAK-169 slowly through the vein (infusion). This will happen once a week during a 28-day cycle. Different small groups of participants will receive lower to higher doses of TAK-169. The study doctors will check for side effects after each dose of TAK 169. In this way, researchers can work out the best dose of TAK-169 to give participants in Part 2 of the study. Each participant will stay in the clinic for at least 24 hours after they have received their first infusion of TAK-169. Once the best dose has been worked out, different small groups of participants will receive lower to higher doses of TAK-169 every 2 weeks, starting at the best dose. In Part 2, at the first visit, the study doctor will check who can take part, as only some participants with multiple myeloma can take part. Participants who previously did not respond to daratumumab or it worked for a while but stopped working, over time will have 1 of 2 treatments. - Some will receive TAK-169 once a week. - Others will receive TAK-169 every 2 weeks. Participants who have never previously received other medicines that bind to the multiple myeloma CD38 cells can also take part. They will receive TAK-169 once a week. All participants in Part 2 will receive the best dose of TAK-169 worked out in Part 1. In both parts of the study, participants can receive TAK-169 for up to 1 year. They could receive TAK-169 for longer than 1 year if their multiple myeloma continues to improve or remains stable during treatment. After treatment has finished, participants will visit the clinic for a check-up every 12 weeks.