Ketamine With Dialectical Behavioural Therapy (DBT) for Suicidality in Individuals With Treatment-Resistant Depression and Borderline Personality Disorder (KET-DBT)

The goal of this clinical trial is to learn if intravenous (IV) ketamine with Dialectical Behavioural Therapy (DBT) reduces suicidal ideation in individuals with suicidality who have been diagnosed with Borderline Personality Disorder and either Major Depressive Disorder or Bipolar Disorder. The main question it aims to answer is: Does IV ketamine and DBT produce more rapid and robust improvements in suicidal ideation (SI) severity between baseline and Day 35 compared to IV midazolam and DBT, as measured by changes in the Modified Scale for Suicidal Ideation (MSSI) scores ? Researchers will compare six IV ketamine infusions and DBT to an active placebo (a look-alike substance that mimics some of ketamine's effects and not others) and DBT to see if IV ketamine with DBT is more effective at reducing SI severity. Participants will: * Complete six infusions of either IV ketamine or IV midazolam * Take part in 6 months of DBT (includes both weekly one-on-one sessions, and group sessions, starting week 5 of the trial) * Visit the hospital for scheduled in-person visits * Join a call or videocall for scheduled remote visits * Complete a variety of different mood, cognitive and behavioral assessments