This is a Trial of MG1-E6E7 With Ad-E6E7 and Atezolizumab in Patients With HPV Associated Cancers

Key Inclusion Criteria:

* Histologically or cytologically confirmed recurrent or metastatic HPV associated tumor (cervical, oropharyngeal, vulvar, vaginal, anal, or penile) with documented disease progression.
* Arm 1, Phase 1 dose escalation: Cervical, HPV+ oropharyngeal, vulvar, vaginal, anal, or penile
* Arm 1, Cohort A: Cervical cancer
* Arm 1, Cohort B: HPV+ Oropharyngeal cancer
* Arm 2 Phase 1 dose escalation and Cohort C: Cervical, oropharyngeal, vulvar, vaginal, anal, or penile
* Failed, refused or intolerant to systemic therapy
* Measurable disease based on RECIST 1.1
* At least one tumor mass amenable to core needle biopsy
* Arm 2 only: At least one tumor judged as being safely injectable
* ECOG performance status 0 or 1
* Demonstrate adequate organ function
* Additional Inclusion criteria exist

Key Exclusion Criteria:

* Prior systemic therapy within 4 weeks.
* Patients receiving prior XRT must have recovered from any acute toxicity.
* Currently receiving/received experimental therapy within 4 weeks.
* Prior treatment with any HPV vaccine therapy for cancer.
* Requires use of anti-platelet or anti-coagulant therapy that cannot be safely suspended for per protocol biopsies or intra-tumoral injections.
* Known active CNS metastases and/or carcinomatous meningitis.
* Clinically significant tumor invasion/ rapidly accumulating ascites, pericardial or pleural effusions.
* Active infection requiring systemic therapy.
* Active autoimmune disease that has required systemic therapy in the past 2 years.
* Conditions likely to have resulted in splenic dysfunction.
* Known HIV/AIDS, active HBV or HCV infection.
* Received prior treatment with vesicular stomatitis (VSV) viral vector.
* Received immunosuppressive medication within 4 weeks. (\>10mg/day prednisone)
* ≥ Grade 2 dyspnea and/or require supplemental oxygen
* Known intolerance to anti-PD-1 or anti-PD-L1 antibody therapy
* Additional Exclusion criteria exist

Exclusion Criteria Household Contacts:

* Patients with household contacts meeting any of the following criteria are ineligible for study entry unless alternate living arrangements can be made, while under contact precautions.
* Women who are pregnant or nursing an infant
* Children \< 1 year old
* Individuals who are severely immunocompromised
* Contact precautions are from initial treatment with MG1-E6E7 to 7 days after the last dose of MG1-E6E7