Thrombotic thrombocytopenic purpura (or TTP for short) is a condition where blood clots form in small blood vessels throughout the body. The clots can limit or block the flow of oxygen-rich blood to the body's organs, such as the brain, kidneys, and heart. As a result, serious health problems can develop. The increased clotting that occurs in TTP uses up the cells that help the blood to clot, called platelets. With fewer platelets available in the blood, bleeding problems can also occur. People who have TTP may bleed underneath the skin forming purple bruises, or purpura. TTP also can cause anemia, a condition in which red blood cells break apart faster than the body can replace them, leading to fewer red blood cells than in normal.

TTP is caused by a lack of activity in the ADAMTS13 enzyme, a protein in the blood involved in controlling clotting of the blood. The ADAMTS13 enzyme breaks up another blood protein called von Willebrand factor that forms blood clots by clumping together with platelets. Some people are born with this condition, while others develop the condition during their life. Many people who are born with TTP experience frequent flare-ups that need to be treated right away. TAK-755 is a medicine that replaces ADAMTS13 and may prevent or control TTP flare-ups, called acute TTP events.

The main aim of the study is to check for side effects of long-term treatment with TAK-755. Treatment will be given in 2 ways:

1. TAK-755 treatment given either every week or every other week to prevent acute TTP events from happening (the "prophylactic" cohort).
2. TAK-755 treatment given to control an acute TTP event when it happens (the "on-demand" cohort).

Participants in the prophylactic cohort will receive treatment in the clinic or at home for up to approximately 3 years. They will visit the clinic at least every 12 weeks. Participants in the on-demand cohort will receive daily treatment for the acute TTP event until the flare-up has gotten better. They will have a follow-up visit at the clinic 4 weeks later.

This is a follow-up study to the Phase 3 pivotal study (281102 [NCT03393975]) and will be comprised of two treatment cohorts (Prophylactic and On-demand) consisting of naïve and non-naïve participants who were born with TTP, with a total duration of approximately 6 years. A maximum of approximately 77 participants will be enrolled in this study (approximately 57 participants who have completed study 281102 [NCT03393975] [non-naïve participants] and at least 20 naïve participants (participants who are naïve to TAK-755). Participants from Expanded Access Programs, participants from study 281102 (NCT03393975) who had an allergic reaction to standard of care treatment, and participants who completed the Phase 1 study (281101 [NCT02216084]) but did not participate in Study 281102, will also be eligible for enrollment in this continuation study as naïve participants.

TAK-755 is given slowly through a vein (intravenous infusion). Participants in the prophylactic cohort will be able to opt for treatment in a home setting by caregiver or self-infusion subject to conditions and to local regulatory approval.

Inclusion Criteria:

Participants who have completed TAK-755 Phase 3 pivotal Study 281102 (NCT03393975) in the prophylactic cohort and who meet all of the following criteria are eligible for this study:

• Participants or legally authorized representative has provided signed informed consent >=18 years of age and/or assent form <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 ADAMTS-13 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 × ULN at screening (prophylactic cohort only).
• Participants >=16 years of age must have a Karnofsky score >= 70% 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.

All naïve participants and non-naïve on-demand cohort participants:

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. Naïve pediatric participants can be enrolled after enrollment of the respective age cohort into the pivotal Phase 3 study 281102 (NCT03393975) has been completed. The following criteria also applies to participants who completed study 281101 (NCT02216084), but did not participate in 281102 (NCT03393975).

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 criteria are eligible for this study:

• Participant is naïve or was enrolled into the on-demand cohort of the TAK-755 Phase 3 pivotal study 281102 (NCT03393975) for treatment of an acute TTP event but did not receive prophylactic treatment.

• Participant or legally authorized representative has provided signed informed consent (>=18 years of age) and/or assent form (<18 years of age).

• Participant is 0 to 70 years of age at the time of screening.

• Participant has been diagnosed with severe congenital ADAMTS-13 deficiency defined as:

  • Confirmed by molecular genetic testing, documented in participant history or at screening, and
  • ADAMTS-13 activity <10% as measured by the fluorescence resonance energy transfer (FRETS)-VWF73 assay, documented in participant history or at screening. Participants currently receiving standard of care prophylactic therapy may exceed 10% ADAMTS-13 activity at screening.

• Participants currently receiving prophylactic therapy will be screened immediately prior to their usual prophylactic infusion.

• Participant does not display any severe TTP signs (platelet count <100,000/microliter (mcL) and elevation of LDH >2 × ULN) at screening (prophylactic cohort only).

• Participants >=16 years of age must have a Karnofsky score >=70% and participants <16 years of age must have a Lansky score >=80%.

• Participants is hepatitis C virus negative (HCV-) as confirmed by antibody or polymerase chain reaction testing OR HCV positive (HCV+) if their disease is chronic but stable.

• 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 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.

Participants from an Expanded Access Program or participants in Study 281102 (NCT03393975) who had an allergic reaction to standard of care prophylactic treatment must meet all of the following criteria:

Participants from an expanded access program as well as participants who participated in Study 281102(NCT03393975) who had an allergic reaction to standard-of-care prophylactic treatment are eligible for enrollment in the continuation study if they meet ALL of the following criteria.

• Participants or legally authorized representative has provided signed informed consent (>=18 years of age) and/or assent (<18 years of age).

• Participants is 0 to 70 years of age at the time of screening.

• Participants has been diagnosed with severe congenital ADAMTS-13 deficiency defined as:

  • Confirmed by molecular genetic testing, documented in participant history or at screening, and
  • ADAMTS-13 activity <10% as measured by the fluorescence resonance energy transfer (FRETS)- VWF 73 assay, documented in participant history or at screening. Participants currently receiving standard of care prophylactic therapy may exceed 10% ADAMTS 13 activity at screening.

• Participant does not display any severe TTP signs (platelet count <100,000/mcL and elevation of LDH >2 × ULN) at screening (prophylactic cohort only).

• Participants >=16 years of age must have a Karnofsky score >=70% 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 highly effective 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 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.

Exclusion Criteria:

Participants who have completed TAK-755 Phase 3 pivotal study (281102) (NCT03393975) and naïve participants and non-naïve on-demand cohort participants and participants from an Expanded Access Program or participants in Study 281102 (NCT03393975) who had an allergic reaction to standard-of-care prophylactic treatment. The following criteria also applies to participants who completed study 281101 (NCT02216084), but did not participate in 281102 (NCT03393975).

• 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 ADAMTS-13, hamster protein, or other constituents of TAK-755.

• Participant has a presence of a functional ADAMTS-13 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:

  • Serum alanine aminotransferase >= 2 × ULN
  • Severe hypoalbuminemia <24 gram per liter (g/L)
  • Portal vein hypertension (e.g., presence of otherwise unexplained splenomegaly, history of esophageal varices).

• In the opinion of the investigator, the participant has another clinically significant concomitant disease that may pose additional risks for the participant.

• Participant has been treated with an immunomodulatory drug, excluding topical treatment (e.g., ointments, nasal sprays), within 30 days prior to enrollment. Use of corticosteroids in conjunction with administration of fresh frozen plasma to prevent allergic reactions is permitted.

• Participant has an acute illness (e.g., influenza, flu-like syndrome, allergic rhinitis/conjunctivitis, bronchial asthma) at the time of screening (prophylactic cohort only).

• Participant is receiving or anticipates receiving another investigational drug and/or interventional drug within 30 days before enrollment.

• Participant has a history of drug and/or alcohol abuse within the last 2 years.

• Participant has a progressive fatal disease and/or life expectancy of <= 3 months.

• Participant is identified by the investigator as being unable or unwilling to cooperate with study procedures.

• Participant suffers from a mental condition rendering him/her unable to understand the nature, scope, and possible consequences of the study and/or evidence of an uncooperative attitude.

• Participant is a family member or employee of the sponsor or investigator.

• If female, participant is pregnant or lactating at the time of enrollment.

• In the UK only: Participants who have not previously received a dose of TAK-755.

Takeda provides access to the de-identified individual participant data (IPD) for eligible studies to aid qualified researchers in addressing legitimate scientific objectives (Takeda's data sharing commitment is available on https://clinicaltrials.takeda.com/takedas-commitment?commitment=5). These IPDs will be provided in a secure research environment following approval of a data sharing request, and under the terms of a data sharing agreement.

IPD from eligible studies will be shared with qualified researchers according to the criteria and process described on https://vivli.org/ourmember/takeda/. For approved requests, the researchers will be provided access to anonymized data (to respect patient privacy in line with applicable laws and regulations) and with information necessary to address the research objectives under the terms of a data sharing agreement.