Multi-arm, parallel-group clinical trials are an efficient way of testing several new treatments, treatment regimens or doses. However, guidance on the requirement for statistical adjustment to control for multiple comparisons (type I error) using a shared control group is unclear. We argue, based on current evidence, that adjustment is not always necessary in such situations. We propose that adjustment should not be a requirement in multi-arm, parallel-group trials testing distinct treatments and sharing a control group, and we call for clearer guidance from stakeholders, such as regulators and scientific journals, on the appropriate settings for adjustment of multiplicity.