Inclusion Criteria:

• Performance status
• Life expectancy > 3 months
• Relapsed or refractory multiple myeloma. Participants with primary refractory myeloma only allowed in dose-escalation phase of the study.
• Treated with at least three prior lines of multiple myeloma therapy including a proteasome inhibitor and an immuno modulatory agent or who are double refractory to a proteasome inhibitor and an immuno modulatory agent. Prior daratumumab treatment is acceptable only for participants receiving monotherapy treatment.
• Treatment with prior autologous transplant is permitted
• Documented diagnosis of symptomatic multiple myeloma, as defined by the International Myeloma Working Group (IMWG)
• Measurable disease defined as at least one of the following: serum M-protein >/=1 grams/deciliter (g/dL), urine M-protein >/= 200 milligrams/24 hours (mg/24h), serum free light chain (SFLC) assay: involved SFLCs >/= 10 mg/dL (>/= 100 mg/L) and an abnormal SFLC ratio (<0.26 or >1.65).
• Female participants of childbearing potential must have a negative serum pregnancy test within the 7 days prior to the first study drug administration.
• For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods that result in a failure rate of
• For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures and agreement to refrain from donating sperm, as defined: With female partners of childbearing potential or pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 4 months after the last dose of RO6870810 as monotherapy, or for at least 3 months after the last dose of daratumumab.

Exclusion Criteria:

• Plasma cell leukemia defined as peripheral plasma cell count > 2000/cubic millimeter (mm^3)
• For expansion cohorts only: Primary refractory multiple myeloma defined as disease that is non-responsive in participants who have never achieved a minimal response or better with any therapy
• History of other malignancy within 2 years prior to screening, except for ductal carcinoma in situ not requiring chemotherapy, appropriately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, low-grade, localized prostate cancer (Gleason score
• POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein and skin changes)
• Current or prior disease or treatment that could compromise protocol objectives in the opinion of the Investigator and/or the Sponsor
• Pregnant or breastfeeding female.
• Prior treatment with any anti-CD38 therapy, including daratumumab (for participants receiving RO6870810 and daratumumab combination treatment)
• Prior treatment with small molecule BET family inhibitor or receiving steroids >the equivalent of 10mg prednisone daily
• participants who are currently receiving any other investigational agent or have received an investigational agent within 30 days or 5 half-lives, whichever is longer, prior to study entry
• Uncontrolled cancer pain