Pembrolizumab With Chemotherapy for Poorly Chemo-responsive Thyroid and Salivary Gland Tumors

Inclusion Criteria: * Patients must have histologically confirmed disease that is unresectable and not amenable to curative intent therapy: 1. Cohort A: salivary gland cancers (mucoepidermoid carcinoma, adenocarcinoma, adenoidcystic carcinoma, acinic cell carcinoma, or other histology) originating in salivary glands. 2. Cohort B: thyroid cancer, RAI-refractory and after failure, intolerance to or refusal of anti-antiangiogenic therapy, or with evidence of dedifferentiated or anaplastic histology. * ECOG performance status 0 or 1. * Consent to undergo on treatment biopsy if tumor is accessible and safe to biopsy * Measurable disease per RECIST 1.1, bone only metastatic disease may be allowed on approval from study PI. * Life expectancy of greater than 12 weeks. * Available tissue for PD-L1 staining (archival or new core needle biopsy at baseline if no archival tissue available). A minimum of 10 slides are required (unless approval from the PI is obtained) * Age greater than or equal to 18 years on day of signing informed consent. * Demonstrate reasonable organ function as defined in Table 1, all screening labs should be performed within 10 days of treatment initiation. System Laboratory Value Hematological Absolute neutrophil count (ANC) ≥1,500 /mcL Platelets ≥100,000 / mcL Hemoglobin ≥9 g/dL or ≥5.6 mmol/L without transfusion or EPO dependency (within 7 days of assessment) Renal Serum creatinine OR ≤1.5 X upper limit of normal (ULN) OR Measured or calculateda creatinine clearance ≥40 mL/min for subject with creatinine levels \> 2.0 X (GFR can also be used in place of creatinine or CrCl) institutional ULN Hepatic Serum total bilirubin ≤ 1.2 X ULN OR in case of Gilbert's disease an elevated total Bilirubin is allowed if direct Bilirubin is ≤40% of total AST (SGOT) and ALT (SGPT) ≤ 2.5 X ULN Coagulation International Normalized Ratio (INR) or ≤1.5 X ULN unless subject is receiving anticoagulant therapy Prothrombin Time (PT) as long as PT or PTT is within therapeutic range of intended use of anticoagulants Activated Partial Thromboplastin Time (aPTT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants aCreatinine clearance should be calculated per institutional standard. * Female subjects of childbearing potential should have a negative urine or serum pregnancy test within 72 hours of receiving first dose of study treatment. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy. Abstinence is considered an acceptable method of contraception. Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 2 weeks of the first dose of treatment. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy in excess of prednisone 10mg/24h equivalent, or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * Has a known history of active TB (Bacillus Tuberculosis) * Has hypersensitivity to pembrolizumab, docetaxel or any of its excipients. * Has had a prior anti-cancer monoclonal antibody (mAb) within 3 weeks prior to study Day 1, or targeted small molecule therapy within 2 weeks prior to study Day 1, or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier, with the exception of lymphopenia or asymptomatic aberrancies of sodium, amylase, lipase or alkaline phosphatase. * Has not recovered from prior surgery, chemotherapy or radiation therapy from adverse events due to a previous treatment/administered agent (i.e., ≤ Grade 1 or return to baseline prior to treatment). * Note: Subjects with ≤ Grade 2 neuropathy, any grade hearing loss or tinnitus, or typical side effects from radiotherapy are an exception to this criterion and may qualify for the study. * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical or other cancers that are not likely to influence life expectancy in the subsequent 3 years without active treatment (e.g. low grade prostate cancer in absence of therapy). * Has known active (growing) central nervous system (CNS) metastases and/or carcinomatous meningitis. Prior radiation or resection is acceptable if clinically stable for at least 4 weeks. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids in excess of prednisone 10mg/24h equivalent or immunosuppressive drugs) and would represent significant morbidity risk in judgement of investigator. Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Has known history of, or any evidence of, active non-infectious pneumonitis. * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * Has a known history of Human Immunodeficiency Virus (HIV) infection (HIV 1/2 antibodies). Patients with treated HIV, as evidenced by stable CD4 \> 200 for at least 6 months, are eligible. * Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Has received a live vaccine within 30 days of planned start of study therapy. * History of organ transplant that requires use of immunosuppressives. * Any condition that would jeopardize the safety of the subject or compliance with the Protocol. * Clinically significant cardiac disease, including unstable angina, acute myocardial infarction within 6 months from Day 1 of study drug administration, New York Heart Association Class III or IV congestive heart failure, and arrhythmia requiring therapy Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed within 30 days prior to initiation of treatment.