 Collectively, patients representing 3 different vWF-related platelet function disorders: TTP in remission, acute TTP, and vWD-2b will be treated in a total of 5 cohorts. Three cohorts will consist of patients who are status post an episode of TTP TTP Remission Cohorts and will be treated with ARC1779 Injection in a dose- and duration-escalation design. In parallel, a single cohort of patients with acute TTP Acute TTP Cohort will be treated according to an individual patient titration-to-response paradigm. This cohort will be opened for enrollment at the beginning of the study and closed after all of the other cohorts are completed. Also in parallel, a single cohort of patients with vWD-2b vWD-2b Cohort will begin enrollment at the commencement of the study and continue independently of the course of the TTP Remission Cohorts. Up to 4 patients will be included in each of the TTP cohorts. The vWD-2b Cohort is expected to consist of up to 12 vWD-2b patients. 