Inclusion Criteria:

          -  Written informed consent

          -  Age >/= 18 years

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2

          -  Patients for whom no standard curable therapy exists

          -  Life expectancy of >/= 12 weeks

          -  Last dose of systemic anti-neoplastic therapy > 21 days prior to first RO6927005
             infusion

          -  Palliative radiotherapy is allowed up to 2 weeks before the first RO6927005 infusion;
             palliative 8 Gy radiotherapy is allowed during therapy.

          -  All acute toxic effects of any prior radiotherapy, chemotherapy, or surgical procedure
             must have resolved to Grade </= 1, except alopecia (any grade) and Grade 2 peripheral
             neuropathy

          -  Adequate hematological, liver, and renal function

          -  Negative serum or urine pregnancy test within 7 days prior to study treatment in
             premenopausal women and women </= 2 years after menopause (menopause is defined as
             amenorrhea for >/= 2 years)

          -  Agreement to use adequate contraceptive methods per protocol

          -  Measurable and/or evaluable disease as per the Response Evaluation Criteria In Solid
             Tumors (RECIST) version 1.1) [Groups 1, 2 of Part A and Group 3 of Part B]

        Inclusion Criteria Part A: MAD

          -  Metastatic and/or locally advanced malignant solid tumors enriched in tumor types
             known to be mesothelin expressing

          -  Archival sample or fresh biopsy or tumor effusion must be available for retrospective
             mesothelin analysis

        Inclusion Criteria Part A: MAD and Extension Phase (Group 1 and Group 2)

          -  Histologically confirmed metastatic and/or advanced malignant mesothelin-positive
             solid tumors as determined by central pathology lab review

          -  Patients must be willing to provide a screening and post-dose biopsy for biomarker
             analysis (extension phase only)

          -  Mesothelin-positive refractory/recurrent solid tumors, other than malignant pleural
             mesothelioma (MPM) and pancreatic ductal adenocarcinoma (PDA) (Group 1 only)

          -  Mesothelin-positive refractory/recurrent MPM (Group 2 only)

        Inclusion Criteria Part B

          -  Histologically confirmed metastatic and/or advanced mesothelin-positive PDA as
             determined by central pathology lab review

          -  In the extension phase, patients must be willing to provide a screening and post-dose
             biopsy for biomarker analysis

        Exclusion Criteria:

          -  Known or clinically suspected central nervous system (CNS) primary tumors or
             metastases including leptomeningeal metastases; history or clinical evidence of CNS
             metastases unless they have been previously treated, are asymptomatic, and have had no
             requirement for steroids or enzyme-inducing anticonvulsants in the last 14 days

          -  Evidence of significant, uncontrolled concomitant diseases which could affect
             compliance with the protocol or interpretation of results, including significant
             pulmonary disease other than primary cancer, uncontrolled diabetes mellitus, and/or
             significant cardiovascular disease (such as New York Heart Association Class III or IV
             cardiac disease, myocardial infarction within the last 6 months, unstable arrhythmias,
             unstable angina, or clinically significant pericardial effusion)

          -  Active or uncontrolled infections

          -  Known HIV or known active HBV or HCV infection

          -  Patients with extrapleural pneumonectomy (EPP)

          -  Any other diseases, metabolic dysfunction, physical examination finding, or clinical
             laboratory finding giving reasonable suspicion of a disease or condition that would
             contraindicate the use of an investigational drug

          -  Major surgery or significant traumatic injury < 28 days prior to the first RO6927005
             infusion (excluding biopsies) or anticipation of the need for major surgery during
             study treatment

          -  Dementia or altered mental status that would prohibit informed consent

          -  Live attenuated vaccinations 14 days prior to treatment

          -  Pregnant or breast-feeding women

          -  Known hypersensitivity to any of the components of RO6927005

          -  High doses of systemic corticosteroids within 7 days prior to first dosing. High dose
             is considered as > 20 mg of dexamethasone a day (or equivalent) for > 7 consecutive
             days

        Exclusion Criteria (Part B):

          -  Patients with contra-indication and/or history of severe hypersensitivity reactions to
             gemcitabine and/or nab-paclitaxel as mentioned in the locally approved label