Inclusion Criteria:  Informed consent signed by the subject prior to conducting study-specific procedures. Male or female subjects ≥ 18 years of age.  Histological diagnosis as follows:  Part A (dose-escalation): histological diagnosis of any type of carcinoma, sarcoma, or melanoma with progressive metastatic disease, or progressive locally advanced disease not amenable to local therapy. Part B (tumor-type-specific expansion Cohorts): histological diagnosis of the relevant tumor type (NSCLC, SCCHN, TNBC, melanoma) with advanced/metastatic disease not amenable to local therapy. Part C (combination cohort): histological diagnosis of NSCLC or melanoma with advanced/metastatic disease not amenable to local therapy. Subjects must be eligible to receive a PD-1 or PD-L1 inhibitor. Part D (biology cohort): histological or cytological diagnosis of any type of carcinoma, sarcoma, or melanoma with progressive metastatic disease, or progressive locally advanced disease not amenable to local therapy.  Prior therapies:  a. Part A (dose-escalation)  i. For the escalation cohorts, subjects must have experienced PD on an established standard systemic anti-cancer therapy for a given tumor type or have been intolerant to such therapy, or in the opinion of the Investigator have been considered ineligible for a particular form of standard therapy on medical grounds. Subjects must have no available proven curative or life-prolonging therapies.  b. Part B (dose-expansion)  i. For NSCLC: subjects must have received platinum-based therapy and a PD-1 or PD-L1 inhibitor unless contraindicated. Subjects eligible for mutation-targeted therapies to EGFR, ALK, ROS, RET, or NTRK (e.g., crizotinib) must have exhausted such therapies. Prior therapies may have been administered alone or in combination. No more than 2 chemotherapy regimens are allowed.  ii. For SCCHN: subjects must have received one line of chemotherapy and a PD-1- or PD-L1-targeted agent alone or in combination with chemotherapy unless contraindicated. No more than 2 chemotherapy regimens in the advanced setting are allowed.  iii. For TNBC: subjects must have received one line of chemotherapy and a PARP inhibitor (if eligible based on BRCA mutation status) in the metastatic or locally advanced unresectable setting. Eligible subjects may have received a PD-(L)1 inhibitor.  iv. For melanoma: subjects must have received a PD-1 or PD-L1 inhibitor, alone or in combination with a CTLA-4-targeted therapy. Eligible subjects must have received BRAF- and MEK-targeted therapies.  c. Part C (combination cohort): subjects with histologically confirmed unresectable locally advanced or metastatic NSCLC or melanoma requiring systemic therapy who are eligible for anti-PD-1 monotherapy and have not received prior anti-PD-1 or anti-PD-L1 therapy:  i. For NSCLC, subjects may have received platinum-based therapy for advanced disease. Subjects eligible for mutation-targeted therapies to EGFR, ALK, ROS, RET, or NTRK (e.g., crizotinib) must have exhausted such therapies.  ii. PD-1 or PD-L1 given in the adjuvant setting is allowed provided that 6 months has elapsed from the end of such therapy to the first dose of OR2805.  d. Part D (biology cohort): subjects must have experienced PD on an established standard medical anti-cancer therapy for a given tumor type or have been intolerant to such therapy, or in the opinion of the Investigator have been considered ineligible for a particular form of standard therapy on medical grounds and must have no available demonstrated curative or life-prolonging therapies.  Subject must have demonstrated PD after the most recent treatment regimen (not applicable to Part C). Subjects must have measurable disease as per RECIST v1.1. Subjects in Part D must have one lesion amenable to biopsy and not to be used for response assessment as per RECIST v1.1. If not postmenopausal or surgically sterile, subjects must be willing to practice at least one highly effective method of birth control for at least a menstrual cycle (or partner's menstrual cycle, for male subjects) before and for 3 months after study medication administration. Resolution of prior-therapy-related AEs (including immune-related AEs but excluding alopecia grade ≤ 2 peripheral neuropathy is allowed) to ≤ grade 1 per CTCAE v5.0, and no treatment for these AEs for at least 2 weeks prior to the time of enrollment, with the exception of electrolyte and hormonal supplementation, which are allowed provided the subject is stable on these supplements. Minimum of 2 weeks since last dose of other hormone therapy and 3 weeks since last dose of other systemic cancer therapy or radiotherapy. Adjuvant hormonal therapy (for example tamoxifen) is allowed provided the original tumor diagnosis was more than 3 years before the first dose of study medication. Subject must have adequate organ function. All subjects must be able to supply an archival tumor biopsy specimen. For Part D (biology cohort), subject has to agree to a newly obtained biopsy of tumor An additional on-treatment biopsy is required for subjects in Part D. Subject is able and willing to comply with the protocol and the restrictions and assessments therein.  Exclusion Criteria:  Subject previously had a severe hypersensitivity reaction to treatment with another mAb. Subject has ECOG PS > 2. Life expectancy <12 weeks. Prior organ or stem cell transplant. Subjects with symptomatic ascites or pleural effusion. Subject has known active CNS primary tumor or metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are clinically stable for at least 4 weeks prior to study entry, have no radiological evidence of new or enlarging brain metastases, and are off steroids or on a stable dose up to an equivalent of prednisone 10 mg/day for at least 15 days prior to first dose of study medication. If subjects have symptoms suspicious for CNS metastasis, an MRI must be negative in the screening period.  Subject has a known history of a hematologic malignancy, malignant primary brain tumor, or another malignant primary solid tumor (other than that under study), unless the subject has undergone potentially curative therapy with no evidence of that disease for at least 3 years.  Note: The time requirement for no evidence of disease for 3 years does not apply to the tumor for which a subject is enrolled in the study. The time requirement also does not apply to subjects who underwent successful definitive resection of basal cell carcinoma of the skin, superficial bladder cancer, squamous cell carcinoma of the skin, in situ cervical cancer, or other in situ cancers.  Recent or ongoing serious infection including the following:  Any uncontrolled grade 3 or higher (per CTCAE v5.0) viral, bacterial, or fungal infection within 2 weeks prior to the first dose of OR2805. Routine antimicrobial prophylaxis is allowed. Uncontrolled infection with HIV. Subjects on stable HARRT therapy with undetectable viral load and normal CD4 counts for at least 6 months prior to study entry are eligible. Serological testing for HIV at screening is not required. Known to be positive for hepatitis B surface antigen, or any other positive test for hepatitis B indicating acute or chronic infection. Subjects who are or have received anti-HBV therapy and have undetectable HBV DNA for at least 6 months prior to study entry are eligible. Known active hepatitis C as determined by positive serology and confirmed by PCR. Subjects on or having received antiretroviral therapy are eligible provided they are virus-free by PCR for at least 6 months prior to study entry. Known active or latent tuberculosis (testing at screening not required). Autoimmune disease or inflammatory condition requiring systemic therapy with exceptions as noted in exclusion criterion 8. Use of systemic corticosteroids within 15 days or other immunosuppressive drugs within 30 days prior to start of the study, with the exception of corticosteroids as replacement therapy up to an equivalent of prednisone 10 mg/day which is allowed. Inhaled, topical, or intraarticular steroids are allowed. Subject has received an investigational product or been treated with an investigational device within 30 days prior to first administration of study medication.  For Part C:  Known contraindication to receiving anti-PD-1 or PD-L1 therapy. Interstitial lung disease. Prior pneumonitis requiring systemic corticosteroid therapy. Receiving immunosuppressive therapy, with exceptions as noted in exclusion criterion 9. A history of severe immune-related adverse reactions from treatment with ipilimumab, defined as any grade 4 toxicity or grade 3 toxicity requiring corticosteroid treatment (> 10 mg/day prednisone or equivalent) for more than 12 weeks. Concurrent therapy with anti-cancer or anti-neoplastic drugs, with the exception of adjuvant hormonal therapy, which is allowed provided the subject has undergone potentially curative therapy with no evidence of that disease for at least 3 years. History or clinical evidence of any surgical or medical condition that the Investigator judges as likely to interfere with the results of the study or pose an additional risk in participating, e.g., rapidly progressive or uncontrolled disease involving a major organ system-vascular, cardiac, pulmonary, gastrointestinal, gynecologic, hematologic, neurologic, neoplastic, renal, endocrine, autoimmune or an immunodeficiency, or clinically significant active psychiatric or abuse disorders. Subject, at the time of signing informed consent, had a recent history (within the last year) of chronic substance abuse. Subject is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study.