Asciminib Treatment Optimization in ≥ 3rd Line CML-CP

This study consists of a screening period of up to 28 days, a treatment period of 144 weeks and a post-treatment safety follow-up period of 4 weeks. Patients will receive asciminib as study treatment continuously for up to 144 weeks or until disease progression, treatment failure or intolerance to treatment. At treatment initiation, asciminib will be provided to all trial patients at a total daily dose of 80 mg. All patients will be randomly assigned 1:1 to 2 groups with 80 mg given either as 40 mg b.i.d. or 80 mg q.d., using IRT to avoid any selection bias. In patients not achieving Major Molecular Responses (MMR) at 48 weeks or losing the response after the week 48 assessment up to week 108, asciminib dose may be escalated to 200 mg q.d. if in the investigator's opinion the patient may benefit from the escalation. In addition, there must not be any grade 3 or 4 toxicity while on therapy, or persistent grade 2 toxicity, possibly related to asciminib and unresponsive to optimal management. The trial will enroll a total of approximately 186 patients: * 156 patients with CML-CP not in MMR at baseline who were treated with two or more TKIs and who were either resistant (ELN 2020 warning or failure) or intolerant to the last treatment will be enrolled. For this population, the primary endpoint for MMR at 48 weeks will be assessed. * Up to 30 additional patients intolerant only to their last TKI treatment and in MMR at baseline will also be enrolled. This patient population will not be part of primary endpoint analysis; however, all assessments will be done as with the 156 patients from the population of the primary endpoint analysis.