Inclusion Criteria:

          -  Incurable HNSCC, defined as RM disease not amenable to cure by surgery and/or
             radiation therapy or patient with HNSCC declines or is ineligible for curative therapy

               -  In phase I, oral cavity, oropharynx, larynx, hypopharynx, nasopharynx, paranasal
                  sinus, or salivary gland

               -  In phase II, oral cavity, oropharynx, larynx, or hypopharynx

          -  Disease Evaluation:

               -  In phase I, evaluable or measurable disease.

               -  In phase II, measurable disease per RECIST 1.1

          -  Prior Treatment:

               -  For phase I, any number of lines of prior therapy for RM-HNSCC.

               -  For phase II, no prior systemic therapy for RM-HNSCC.

          -  At least 18 years of age.

          -  Performance status 0-2 (ECOG).

          -  Adequate blood and organ function as defined:

               -  Absolute neutrophil count ≥ 1,500/mcL

               -  Platelets ≥ 100,000/mcL

               -  Hemoglobin ≥ 9.0 g/dL

               -  Total bilirubin ≤ 1.5 mg/dL

               -  AST(SGOT) ≤ 3 x institutional upper limit of normal (IULN) and ALT(SGPT) ≤ 3 x
                  IULN. In the setting of liver metastases, AST < 5 x IULN and ALT < 5 x IULN.

               -  Creatinine ≤ 2 x ULN OR creatinine clearance ≥ 40 mL/min/1.73 m2

               -  Urine protein to creatinine ratio (UPC) ≤ 1; if UPC ≥ 1, then a 24-hour urine
                  protein must be assessed; patients must have a 24-hour urine protein value < 1 g
                  to be eligible

               -  INR ≤ 1.5 x ULN (≤ 3.0 x ULN if on anticoagulation) and PTT ≤ 1.5 x ULN (<3 x ULN
                  if on anticoagulation) [Patients are allowed to be on anticoagulation]

          -  Women of childbearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control, abstinence) beginning 14 days prior to
             first dose of ramucirumab, through the dosing period, and for at least 28 days after.

          -  Signed IRB approved written informed consent document.

        Exclusion Criteria:

          -  Phase II: prior PD-1 inhibitor for treatment of incurable HNSCC. For phase I, prior
             PD-1 inhibitor therapy in the incurable setting is permitted.

          -  Radiation, chemotherapy, targeted or investigational therapy within 14 days of
             treatment start.

          -  Major surgery, presence of a non-healing, non-malignant ulcer within 14 days of
             treatment start; History of significant tumor site bleeding within 14 days of study
             consent.

          -  History of other malignancy ≤ 1 year previous with the exception of completely
             resected skin carcinoma or other cancers with a low risk of recurrence.

          -  Cirrhosis at a level of Child-Pugh B (or worse), Cirrhosis of any degree with a
             history of hepatic encephalopathy or clinically meaningful ascites (from cirrhosis
             requiring diuretics or paracentesis).

          -  Receiving any other investigational agents.

          -  Ongoing toxicity attributed to prior anti-cancer therapy that is > grade 1, except
             alopecia, anemia, fatigue or rash.

          -  Active central nervous system metastases: defined as currently receiving radiation
             therapy to metastatic CNS disease. Once radiation therapy is completed, patients with
             CNS disease are eligible if they meet all other criteria for enrollment.

          -  History of severe allergic reactions attributed to agents used in the study.

          -  Serious uncontrolled inter-current illness within the 3 months prior to study entry or
             psychiatric illness/social situations that would limit compliance with study
             requirements.

          -  Receiving systemic steroid therapy (in dosing exceeding 20 mg daily of prednisone
             equivalent) or any other form of immunosuppressive therapy within 7 days prior to the
             first dose of pembrolizumab.

          -  Has an active autoimmune disease (i.e. rheumatoid arthritis, lupus, Sjogren's
             syndrome) that has required IV or subcutaneous systemic treatment in the past 6 months
             (excluding rituxin). Replacement therapy (i.e. thyroxine, insulin, or physiologic
             corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is
             not considered a form of system treatment.

          -  GI perforation or fistula within 6 months of first dose of protocol therapy

          -  History of GI issues such as inflammatory bowel disease, ulcerative colitis, or
             Crohn's disease.

          -  Poorly controlled hypertension (defined as high blood pressure measurements [systolic
             blood pressures of ≥ 160 mmHg or diastolic blood pressures of > 100 mmHg] documented
             during the two-week interval prior to enrollment). Initiation or adjustment of
             antihypertensive medications to control blood pressure is permitted prior to study
             entry.

          -  Arterial thromboembolic events (including but not limited to myocardial infarction,
             transient ischemic attack, cerebrovascular accident, or unstable angina) within 3
             months prior to first dose of treatment.

          -  GI Bleeding (grade 3 or 4) within 3 months prior to first dose.

          -  Pregnant and/or breastfeeding. Patient must have a negative serum pregnancy test
             within 7 days of first dose of treatment.