A Study Evaluating the Effects of GLPG3667 Given as Oral Treatment for up to 24 Weeks in Adults With Dermatomyositis

Key Inclusion Criteria: * Participant has probable or definite DM in accordance with the ACR/EULAR criteria for at least 3 months. * Participant with DM diagnosed in the 3 years prior to screening must have undergone cancer screening (according to local standard of care or applicable guidelines) within 1 year prior to screening. Note: The evidence of cancer screening must be documented. * Participant must present objective evidence of active disease as defined by fulfilling 1 of the criteria below (as confirmed by the sponsor): * DM rash as defined by modified-Cutaneous Dermatomyositis Disease Area and Severity Index Activity Score (m-CDASI-A) ≥ 6 at screening, or * Creatine kinase (CK) \> 4x upper limit of normal (ULN) at screening, or * muscle biopsy evidence of active disease within 3 months prior to screening (defined as presence of active inflammation in muscle biopsy), or * muscle magnetic resonance imaging showing active inflammation (edema) of the proximal skeletal muscles within 3 months prior to screening, or * electromyography showing acute changes, such as spontaneous activity and myopathic changes not explained by other diseases within 3 months prior to screening, or * any other clinical evidence of active disease as confirmed by the steering committee. * Participant has reduced muscle strength (defined as Manual Muscle Test-8 \< 142/150) and at least 2 additional abnormal core set measurements out of the following 5 at screening: * Physician's Global Disease Activity score \> 2/10 cm on the visual analog scale (VAS), * Patient's Global Disease Activity score \> 2/10 cm on VAS, * extra-muscular disease activity \> 2/10 cm on VAS, * Health Assessment Questionnaire-Disability Index score \> 0.25, * elevated muscle enzymes (e.g. aldolase, CK, ALT, AST, and lactate dehydrogenase) with at least 1 muscle enzyme \> 1.5x ULN. * Participant previously demonstrated failure to or intolerance to first-line treatment (defined as oral corticosteroid\[s\] and at least 1 other immunosuppressant/ hydroxychloroquine) OR active disease despite treatment with first-line drugs. Currently, the participant is receiving maximum 3 treatments for DM (oral corticosteroid\[s\] and/or allowed immunosuppressant\[s\]/hydroxychloroquine) for at least 3 months and is on a stable dose (defined as no change in dose, type of administration, or dose regimen) for at least 4 weeks prior to screening and during screening within maximum allowed doses as specified in the study protocol. Note: Participants receiving 1 or no concomitant treatment for DM are also eligible. * Open Label Extension : Participant must meet both of the following inclusion criteria at Visit 8 to be eligible for participation in the OLE period of the study: participant who may benefit from open-label treatment with GLPG3667, according to the investigator's judgment; participant who completed the 24-week double-blind treatment period on investigational product. Key Exclusion Criteria: * Participant has cancer-associated myositis (defined as myositis diagnosed within 2 years of cancer diagnosis with the exception of basal cell carcinoma, squamous cell carcinoma of the skin, or in situ uterine cervical carcinoma that has been excised and cured). Note: At least 1 year for basal cell carcinoma and squamous cell carcinoma or 5 years for in situ uterine cervical carcinoma must have passed since the excision. * Participant has other causes of myositis (e.g. connective tissue disease) associated DM, polymyositis, juvenile DM, inclusion body myositis, or necrotizing idiopathic inflammatory myopathies (with or without rash) with the exception of overlap with secondary Sjogren's syndrome. * Participant has permanent muscle weakness due to muscle damage (e.g. participant is wheelchair bound or has significant muscle atrophy on magnetic resonance imaging \[MRI\]) or a non-DM cause (drug-induced myopathy, including glucocorticoid-induced myopathy as primary cause of muscle weakness), according to investigator's judgement. * Participant has taken any prohibited therapies within the defined washout periods before screening, and during screening as listed in the study protocol. * Open Label Extension : Participant meeting one or more of the criteria at Visit 8 as defined in the protocol, cannot be selected for the OLE period of this clinical study. 1. Participant has total bilirubin \>1.5x ULN; however, participant with an isolated increase in total bilirubin \<3 x ULN due to Gilbert's Syndrome, with normal direct bilirubin, can be enrolled in the OLE period. 2. Participant has AST or ALT \>1.5 x ULN (hepatic injury), or AST or ALT \>=5 x ULN if judged to be of muscular origin (and confirmed by the steering committee) at Visit 7 and Visit 8.