Key Inclusion Criteria:  Participant with CML-CP that is currently receiving treatment with asciminib, asciminib in combination with imatinib, imatinib alone, nilotinib alone or bosutinib within a Novartis-sponsored study and, in the opinion of the Investigator, would benefit from continued treatment. Participant has demonstrated compliance on the parent study protocol and is willing and able to comply with scheduled visits, treatment plans and any other study procedures.  Key Exclusion Criteria:  Participant has been discontinued from parent study treatment. Participant currently has unresolved toxicities reported as possibly related to study treatment in the parent study. Participant's ongoing treatment is currently approved and reimbursed at country level. Pregnant or nursing (lactating) women. Women of child-bearing potential, unless they are using highly effective methods of contraception and willing to continue while taking study treatment. For participants in the USA and on asciminib treatment only: Sexually active males unwilling to use a condom during intercourse while taking study treatment.  Applicable only for participants on bosutinib treatment that switch to asciminib treatment at enrollment:  Asymptomatic pancreatitis abnormal ECG  Other protocol-defined Inclusion/Exclusion criteria may apply.