Phase 3 Study of Adjunctive Treatment With Seltorexant in Adult and Elderly Participants With Major Depressive Disorder and Insomnia Symptoms

Inclusion Criteria: Participants in part 1 and direct enrollers to part 2: * Meet DSM-5 MDD, without psychotic features based upon clinical assessment and confirmed by the structured clinical interview for DSM-5 Axis I disorders-clinical trials version (SCID-CT) diagnosed with first depressive episode prior to age 60 * Have had an inadequate response to at least 1 but no more than 2 antidepressants, administered at an adequate dose and duration in the current episode of depression. An inadequate response is defined as less than (\<) 50% reduction but with some improvement (that is, improvement greater than \[\>\] 0%) in depressive symptom severity with residual symptoms other than insomnia present, and overall good tolerability, as assessed by the MGH-ATRQ, and this must include the participant's current antidepressant treatment * Is receiving and tolerating well any one of the following SSRI or SNRI for depressive symptoms at screening, in any formulation and available in the participating country: citalopram, duloxetine, escitalopram, fluvoxamine, fluoxetine, milnacipran, levomilnacipran, paroxetine, sertraline, venlafaxine, desvenlafaxine, vilazodone, or vortioxetine at a stable dose (at therapeutic dose level) for at least 6 weeks * Having a major depressive episode of at least moderate severity, as assessed with 17-item Hamilton Depression Rating Scale, implemented through the Structured Interview Guide (SIGH-D) in a blinded manner at screening and must not demonstrate a clinically significant improvement from the beginning to end of screening. Participants entering after completing part 1: * Must have completed Part 1 DB treatment phase * Can consistently tolerate study drug (at the end of Part 1), and there is no additional safety risk for the participant if they proceed to Part 2 * Was able to consistently follow the study procedures in Part 1 as judged by the investigator. * Must be medically stable based on clinical laboratory tests Exclusion Criteria: * Has a recent (last 3 months) history of, or current signs and symptoms of, severe renal insufficiency clinically significant or unstable cardiovascular, respiratory, gastrointestinal, neurologic, hematologic, rheumatologic, immunologic or endocrine disorders and uncontrolled Type 1 or Type 2 diabetes mellitus * Has a history of narcolepsy and seizures * Has current signs/symptoms of hypothyroidism or hyperthyroidism * Participants taking thyroid supplementation for antidepressant purposes * Has Cushing's disease, Addison's disease, primary amenorrhea, or other evidence of significant medical disorders of the HPA axis