This multicenter trial has a single arm run-in period followed by a randomized, placebo-controlled, double-blind comparative part. In the single arm part of the trial, patients with HER2-expressing locally advanced or metastatic solid tumours will be enrolled and treated with the antibody-drug conjugate (ADC) SYD985 once every 3 weeks until disease progression or unacceptable toxicity. All patients will receive concomitant BYON5667 eye drops. When the primary safety and efficacy analysis of the BYON5667 eye drops at Day 63 is favorable, the trial may continue to the comparative part in which patients with locally advanced or metastatic HER2-positive breast cancer will be treated with SYD985. Patients will be randomly assigned (1:1) to receive BYON5667 or placebo eye drops.