• 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.