A Research Study to See How Much CagriSema Lowers Blood Sugar and Body Weight Compared to Placebo in People With Type 2 Diabetes Treated With Once-daily Basal Insulin With or Without Metformin

This study will look at how much CagriSema helps people with type 2 diabetes lower their blood sugar and body weight. CagriSema is a new investigational medicine. Doctors may not yet prescribe CagriSema. CagriSema will be compared to a "dummy" medicine (also called "placebo") that has no effect on the body. Participant will get either CagriSema or "dummy" medicine and which treatment they get is decided by chance. Participant will take the study medicine together with their current diabetes medicine (once-daily insulin with or without metformin). For each participant, the study will last for about one year.

Inclusion Criteria: * Male or female (sex at birth). * Age 18 years or above at the time of signing the informed consent. * Diagnosed with type 2 diabetes mellitus ≥180 days before screening. * On stable once-daily dose of basal insulin (minimum of 0.25 units per kilogram per day (U/kg/day) or 20 U/day) alone or in combination with metformin (at effective or maximum tolerated dose as judged by the investigator) for 90 days prior to screening. * Glycated haemoglobin (HbA1c) 7.0-10.5 percent (53-91 millimoles per mole \[mmol/mol\]) (both inclusive) as determined by central laboratory at screening. * Body Mass Index (BMI) greater than or equal to 25 kilogram per square meter (kg/m\^2) at screening. BMI will be calculated in the electronic case report form (eCRF) based on height and body weight at screening. Exclusion Criteria: * Female who is pregnant, breast-feeding or intends to become pregnant or is of childbearing potential and not using a highly effective contraceptive method. * Renal impairment with estimated Glomerular Filtration Rate (eGFR) less than 30 milliliters per minute per 1.73 square meter (mL/min/1.73 m\^2) as determined by central laboratory at screening. * Treatment with any medication for the indication of diabetes or obesity other than stated in the inclusion criteria within 90 days before screening. * Uncontrolled and potentially unstable diabetic retinopathy or maculopathy. Verified by an eye examination performed within 90 days before screening or in the period between screening and randomisation. Pharmacological pupil-dilation is a requirement unless using a digital fundus photography camera specified for non-dilated examination. * Known hypoglycaemia unawareness as indicated by the investigator according to Clarke's questionnaire question 8. * Recurrent severe hypoglycaemic episodes within the last year as judged by the investigator.