Patient description: The patient is a 23-year-old man who came to the hospital with high blood pressure (175/95 mmHg) and signs of septicemia. He developed respiratory failure requiring mechanical ventilation and renal failure requiring hemodialysis. His blood smear showed microangiopathic hemolytic anemia and thrombocytopenia. His blood tests revealed elevated lactate dehydrogenase and reduced human complement C3 levels with a normal coagulation profile. He was diagnosed with atypical hemolytic uremic syndrome. He was treated with plasma exchange and corticosteroids. He has been previously vaccinated with meningococcal group ACWY conjugate vaccine and meningococcal group B vaccine. The genetic survey revealed ADAMTS13 >10%.

Clinical trial eligibility criteria: eligible ages (years): 0.0-70.0,  Congenital Thrombotic Thrombocytopenic Purpura -The participant will not be considered eligible for the study without meeting all of the below: Participants who have completed TAK-755 Phase 3 pivotal study 281102 (NCT03393975) and who meet all of the following are eligible for this study Participants or legally authorized representative has provided signed informed consent (greater than or equal to (>=) 18 years of age) and/or assent form (less than (<) 18 years of age) Participant 0 to 70 years of age at the time of screening of the 281102 (NCT03393975) study Participant has been diagnosed with severe congenital deficiency Participant does not display any severe thrombotic thrombocytopenic purpura (TTP) signs (platelet count < 100,000/ microliter (mcL) and elevation of lactate dehydrogenase (LDH) (greater than) > 2 × upper limit of normal (ULN) at screening (prophylactic cohort only) Participants >= 16 years of age must have a Karnofsky score >= 70 percent (%) and participants < 16 years of age must have a Lansky score >= 80% If female of childbearing potential, participant presents with a negative serum or urine pregnancy test confirmed not more than 7 days before the first IP administration and agrees to employ adequate birth control measures for the duration of the study and to undergo quarterly pregnancy testing Sexually active males must use an accepted and effective method of contraception during the treatment and until a minimum of 16 days after the last dose administered Participant is willing and able to comply with the requirements of the protocol. TAK-755 naïve participants and non-naïve on-demand cohort participants: TAK-755 naïve participants can only be enrolled in this continuation after enrollment of the adult participants in the prophylactic arm of TAK-755 Phase 3 pivotal study 281102 (NCT03393975) has been completed. TAK-755 naive pediatric participants can be enrolled after enrollment of the respective age cohort into the pivotal Phase 3 study 281102 (NCT03393975) has been completed.TAK-755 naïve participants and participants who were enrolled into the on-demand cohort of theTAK-755 Phase 3 pivotal study 281102 (NCT03393975) who meet ALL of the following are eligible for this study Participant is naïve to TAK-755 or was enrolled into the on-demand cohort of the TAK-755 Phase 3 pivotal study 281102 (NCT03393975) for treatment of an acute event but did not receive prophylactic treatment  The participants will be excluded from the study if any of the following are met. For both participants who have completed TAK-755 Phase 3 pivotal study (281102) and TAK 755 naïve participants Participant has been diagnosed with any other TTP-like disorder (microangiopathic hemolytic anemia), including immune-mediated TTP Known life-threatening hypersensitivity reaction, including anaphylaxis, to the parent molecule hamster protein, or other constituents of TAK-755 Participant has a medical history or presence of a functional inhibitor at screening Participant has a medical history of a genetic or acquired immune deficiency that would interfere with the assessment of product immunogenicity, including participants who are human immunodeficiency virus-positive with an absolute cluster of differentiation 4 (CD4) count < 200/ cubic millimeter (mm^3) or who are receiving chronic immunosuppressive drugs Participant has a history of significant neurological events, such as major stroke, indicating that a relapse might have severe consequences, as judged by the investigator Participant has been diagnosed with severe cardiovascular disease (New York Heart Association classes 3 to 4) Participant with end stage renal disease requiring chronic dialysis Participant has been diagnosed with hepatic dysfunction, as evidenced by, but not limited to, any of the following