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Inclusion Criteria:

* Performance status \</=2 on the Eastern Cooperative Oncology Group (ECOG) scale
* Life expectancy \> 3 months
* Relapsed or refractory multiple myeloma. Participants with primary refractory myeloma only allowed in dose-escalation phase of the study.
* Prior treatment: 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 anti-CD38 antibody (e.g., daratumumab, isatuximab) treatment is acceptable only for participants receiving monotherapy treatment.
* Prior treatment: Treated with two or more lines of prior therapy, with disease refractory to both a proteasome inhibitor and an immunomodulatory agent, and disease progression (as defined by International Myeloma Working Group (IMWG) criteria) following treatment with an anti-CD38 monoclonal antibody given as monotherapy or in combination therapy. The most recent treatment regimen must have contained an anti-CD38 monoclonal antibody.
* Treatment with prior autologous transplant is permitted
* Documented diagnosis of symptomatic multiple myeloma, as defined by the 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 \< 1% per year during the treatment period and for at least 2 months after the last dose of RO6870810 as monotherapy, or for at least 3 months after the last dose of daratumumab.
* 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 \</= 7) not requiring treatment or appropriately treated Stage I uterine cancer
* 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.
* Consumption of agents which strongly inhibit CYP3A4 enzyme, within 7 days prior to the first dose of study treatment and during the study.
* Consumption of agents which strongly induce CYP3A4 enzyme, within 14 days prior to the first dose of study treatment and during the study.
* Surgery within 21 days prior to study entry.
* 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
* Prior anti-cancer therapy (chemotherapy, targeted agents, radiotherapy, and immunotherapy) within 14 days except for alkylating agents (e.g., melphalan) within 28 days.

• Duarte, California, United States
• Stanford, California, United States
• Jacksonville, Florida, United States
• Atlanta, Georgia, United States
• Boston, Massachusetts, United States
• New York, New York, United States
• Chapel Hill, North Carolina, United States
• Durham, North Carolina, United States
• Randwick, New South Wales, Australia
• Fitzroy, Victoria, Australia
• London, United Kingdom
• Oxford, United Kingdom