Inclusion Criteria:

• Signed informed consent obtained prior to initiation of any study-specific procedures and treatment.

For dose escalation phase:

• Histologically or cytologically proven metastatic or locally advanced solid tumors for which no standard therapy known to confer clinical benefit exists OR standard therapy has failed recruited from among patients with squamous or non-squamous non-small cell lung cancer
• (NSCLC), squamous cell carcinoma of the head and neck (SCCHN), urothelial carcinoma (UC), metastatic castrate resistant prostate cancer (mCRPC), and metastatic breast cancer (mBC).

For dose confirmation phase:

• Cohort A will enroll patients with metastatic or locally advanced, squamous or non-squamous NSCLC (NSCLC) who had previously received no more than four prior lnes of therapy, including a PD-1/PD-L1 containing therapy and a platinum-containing regimen. Patients must have received no more than one taxane containing regimen and no more than one investigational agent.
• Cohort B will enroll patients with histologically or cytologically confirmed transitional cell carcinoma of the urothelium including bladder, urethra, renal pelvis, or ureter (mUC). Patients must have received no more than three prior regimens, with PD-1 / PD-L1-containing therapy administered as their most recent therapy and have failed to achieve a PR or CR. Additionally for patients that did not progress while on the previous PD-1/PD-L1 containing therapy, the period of SD must be a minimum of four (4) months.
• Patients with metastatic or locally advanced NSCLC, metastatic or locally advanced UC, metastatic or locally advanced SCCHN and mBC must have measurable disease by RECIST criteria, with at least one uni-dimensional measurable lesion.
• Patients with mCRPC must meet PCWG3 criteria for disease progression at trial entry.
• Availability of tumor specimens is optional for patients in dose escalation cohorts and mandatory for patients in the dose confirmation phase. In the dose confirmation phase, an archived formalin-fixed, paraffin-embedded tumor tissue block sufficient in size to allow for sectioning of at least 15 slides should be provided if available from the most recent primary or metastatic tumor biopsy or resection obtained within 3 months prior to start of study therapy. If such an archived sample is not available, a fresh tumor sample must be obtained prior to enrollment. If blocks cannot be provided, then at least 15 freshly prepared slides must be provided. Core needle or excision biopsies are required.
• Male or female patients aged ≥ 18 years at time of informed consent.
• ECOG Performance Status 0 to 1.
• Estimated life expectancy of at least 3 months.
• Adequate bone marrow reserve, hepatic, and renal function, defined by:
  • absolute neutrophil count (ANC) ≥ 1.5 x 10^9/L;
  • platelet count ≥ 100 x 10^9/L;
  • hemoglobin ≥ 9 g/dL (may have been transfused);
  • alanine aminotransferase (ALT, SGPT) ≤ 3.5 x upper limit of normal (ULN);
  • aspartate aminotransferase (AST, SGOT) ≤ 2.5 x ULN;
  • total bilirubin ≤ 1.5 x ULN;
  • calculated creatinine clearance, estimated glomerular filtration rate 9eGFR ≥ 60 mL/min (MDRD formula).
  • normal bood urea nitrogen (BUN) unless considered unrelated to renal dysfunction as assessed by the investigator and Sponsor.
• Female patients of child-bearing potential must have a negative pregnancy test and be nonlactating and use at least one form of contraception as approved by the Investigator for 4 weeks prior to initiating study treatment and continuing for 6 months after the last dose of study drug. For the purposes of this study, child-bearing potential is defined as “all female patients unless they are post-menopausal for at least 3 years or surgically sterile."
• If the risk of conception exists, male patients must use a form of barrier contraception approved by the Investigator during the study and for 6 months after the last dose of study drug.
• Willing and able to comply with study procedures and follow-up.

Exclusion Criteria:

• Concurrent cancer treatment with cytoreductive therapy, radiotherapy, cytokine therapy, cytotoxic agents, or targeted small molecule therapy within 2 weeks prior to the start of study treatment (except 5 weeks from last dose of nitrosourea compound) OR treatment with monoclonal antibodies within 4 weeks prior to the start of study treatment, with the following exceptions:
  • PD-1 / PD-L1 containing checkpoint inhibitor therapy is permitted;
  • palliative bone-directed radiotherapy is permitted unless involving an area of ≥ 25% of bone marrow reserves and occurring within 5 weeks prior to the start of study treatment;
  • erythropoietin and darbopoietin-α are permitted; and
  • hormonal therapies acting on the hypothalamic-pituitary-gonadal axis (i.e., LHRH agonist/antagonist) are permitted. No other hormonal therapy is permitted.
• Known symptomatic central nervous system (CNS) metastases requiring steroids. Patients with previously diagnosed CNS metastases are eligible if they:
  • have completed their treatment and have recovered from the acute effects of radiation therapy and/or surgery prior to enrollment;
  • have discontinued corticosteroid treatment for these metastases for at least 14 days; and
  • are neurologically stable.
• Persisting toxicity related to prior therapy is Grade >1 by NCI-CTCAE v4.03 criteria. However, alopecia or other Grade ≤ adverse events (AEs) not constituting a safety risk based on Investigator’s judgement are acceptable.
• Diagnosis of any other malignancy within 2 years prior to enrollment. However, adequately treated basal cell or squamous cell skin cancer or non-invasive superficial bladder cancer or carcinoma in situ of the bladder, breast or cervix; or prostate cancer of low grade (Gleason ≤ 6) prostate cancer or surveillance without any plans for treatment intervention (e.g., surgery, radiation, or castration) are allowed.
• Prior organ transplantation including allogeneic stem cell transplantation.
• Major surgery (as deemed by the Investigator) for any reason OR not fully recovered from surgery within 4 weeks prior to the start of study treatment.
• Vaccination within 4 weeks of the first dose of study treatment is prohibited except for administration of inactivated vaccines.
• Current use of immunosuppressive medication at study entry, with the following exceptions:
  • intranasal, inhaled, or topical steroids or local steroid injections; (e.g., intra-articular injection) are permitted;
  • systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone or equivalent are permitted; and
  • steroids as premedication for hypersensitivity reactions are permitted.
• Active or prior autoimmune disease that might deteriorate with receiving an immunostimulatory agent. However, patients with diabetes type 1, vitiligo, psoriasis, or hypo- or hyper-thyroid disease not requiring immunosuppressive treatment are eligible.
• Acute or chronic infections requiring systemic therapy, including, among others:
  • active infection requiring systemic therapy;
  • history of testing positive to human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome;
  • hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive HBV surface antigen or HCV RNA if anti-HCV antibody screening test is positive);
  • active tuberculosis (history of exposure or history of positive TB test with presence of clinical symptoms, physical or radiographic finding).
• Clinically significant or active cardiovascular disease, including:
  • ongoing cardiac dysrhythmias of NCI CTCAE v4.03 grade ≥ 2 or prolongation of the QTcF interval to > 450 msec for males, and ≥ 470 msec for females;
  • cerebrovascular accident/stroke < 6 months prior to study entry;
  • myocardial infarction < 6 months prior to study entry;
  • unstable angina;
  • congestive heart failure (New York Heart Association Classification ≥ Class II);
  • symptomatic arrhythmia requiring medication (excluding anemia-related sinusal tachycardia grade ≤ 2 by NCI CTCAE v4.03 criteria). However, subjects with stable atrial fibrillation on treatment are allowed provided they do not meet any other cardiac or prohibited drug exclusion criterion.
• Known history of autoimmune colitis, inflammatory bowel disease, pneumonitis, pulmonary fibrosis.
• Uncontrolled intercurrent illness, including, but not limited to:
  • hypertension uncontrolled by standard therapies;
  • uncontrolled diabetes;
  • Known alcohol or drug abuse;
• Other acute or chronic medical or psychiatric condition including recent (within the past year) or active suicidal ideation or behavior or laboratory abnormality that may increase the risk of study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgement of the Investigator, would make the patient inappropriate for entry into the study.
• Known intolerance to checkpoint inhibitor therapy, defined by the occurrence of an AE leading to drug discontinuation.
• Known prior severe hypersensitivity reaction to monoclonal antibodies (grade ≥ 3 by NCI CTCAE v4.03 criteria).
• Known allergy or hypersensitivity to platinum (Pt)-containing agents, or known intolerance to prior Pt-containing agent which, in the judgement of the Principal Investigator, precludes exposure to Pt-containing agent.
• Known allergic reaction to methotrexate (trace methotrexate may be present in the avelumab drug product).
• Participation in other studies involving investigational drug(s) used to treat malignancy during study participation.
• Legal incapacity or limited legal capacity or any psychiatric condition that would prohibit the understanding or rendering or informed consent or that might limit compliance with study requirements.
• Abnormal blood urea nitrogen (BUN) due to renal compromise or dysfunction (e.g., hydronephrosis).
• Any waiver of these exclusion criteria should be exceptional and justified and must be approved by the Investigator and the Sponsor on a case-by-case basis prior to enrolling the patient. Such waivers must be documented by both the Investigator and Sponsor.