AMD3100 Plus Pembrolizumab in Immune Checkpoint Blockade Refractory Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Have histologically or cytologically confirmed diagnosis of squamous cell carcinoma of the recurrent or metastatic head and neck. For oropharyngeal cancer, tumor HPV status must be known. * Have measurable disease based on RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions * Have progressed on or after immune checkpoint therapy (anti-PD-1 or anti-PD-L1, as a monotherapy or in combination with other agents). Anti-PD-1/PD-L1 immune checkpoint therapy does not have to be the most immediate prior therapy before the study enrollment. * Have provided archival tumor tissue sample or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. If slides are to be submitted, 10-20 unstained slides are required. Newly obtained biopsies are preferred to archived tissue. At a minimum, 3 core biopsies will be obtained and 1 core will be formalin fixed and the other 2 cores will be flash frozen. * Have a lesion that is accessible for biopsy for subjects in the Run-In phase. An exception can be granted for those patients who do not have a lesion that can be safely biopsied based upon review with the Principal Investigator. The tumor biopsy is optional in the Phase II portion of the study * Be \>18 years of age on the day of signing informed consent. * ECOG performance status ≤ 1 (Karnofsky ≥70%, see Appendix A). * Have normal organ and marrow function as defined below. Specimens must be collected within 28 days prior to study registration. * leukocytes ≥3,000/mcL * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * total bilirubin ≤1.5 ×ULN * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional upper limit of normal * creatinine Within normal institutional limits, OR * creatinine clearance ≥60 mL/min/1.73 m2 for participants with creatinine levels above institutional normal. * Ability to understand and the willingness to sign a written informed consent document. * Male participants: A male participant must agree to use a contraception as detailed in Appendix C of this protocol during the treatment period and for at least 120 days after the last dose of study treatment and refrain from donating sperm during this period. -Female participants: A female participant is eligible to participate if she is not pregnant (see Appendix C), not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) as defined in Appendix C, OR * A WOCBP who agrees to follow the contraceptive guidance in Appendix C during the treatment period and for at least 120 days plus 30 days (a menstruation cycle) after the last dose of study treatment. Exclusion Criteria: * Has received prior systemic anti-cancer therapy including investigational agents within 2 weeks prior to registration with the exception of receiving immune checkpoint blockade therapy. * Participants must have recovered from all AEs due to previous therapies to ≤ Grade 1 or baseline. Participants with ≤ Grade 2 neuropathy may be eligible after discussion with PI. * Has received prior radiotherapy within 2 weeks of first dose of study drug. * Participants must have recovered from all radiation-related toxicities to ≤Grade 1 or baseline, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease. * Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 2 weeks prior to the first dose of study drug. Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been \>2 weeks since the last dose of the previous investigational agent. * Has a known diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. * Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g. breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. * Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. * Has severe hypersensitivity (≥Grade 3) to pembrolizumab, AMD3100, and/or any of its excipients. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). 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 a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Has an active infection requiring systemic therapy. * Has a known history of Human Immunodeficiency Virus (HIV). * No HIV testing is required unless mandated by local health authority. * Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. Note: No testing for Hepatitis B and Hepatitis C is required unless mandated by local health authority. * Has a known history of active TB (Bacillus Tuberculosis). * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Has known uncontrolled 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 study, starting with the screening visit through 120 days after the last dose of trial treatment. * A WOCBP who has a positive serum pregnancy test within 72 hours prior to registration (see Appendix C). Note: In the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication.