MG1 Maraba/MAGE-A3, With and Without Adenovirus Vaccine With Transgenic MAGE-A3 Insertion in Incurable MAGE-A3-Expressing Solid Tumours

Inclusion Criteria: * PHASE I: Patients must have histologically confirmed, unresectable locally advanced/metastatic solid tumour with positive expression of MAGE-A3 (primary or metastatic lesion) and for which there is no known life prolonging standard therapy. * PHASE II: Patients must have histologically confirmed, unresectable locally advanced/metastatic solid tumour with positive expression of MAGE-A3 (primary or metastatic lesion) as follows: 1. Non-small cell lung cancer (NSCLC) specifically adenocarcinoma and squamous cell carcinoma. 2. Breast cancer 3. Esophageal/GEJ cancer/gastric * In phase II patients may be treated before refractory, such as while stable post treatment response to first line therapy. * Presence of clinically and/or radiologically documented disease. At least one site of disease must be unidimensionally measurable by CT with IV contrast as follows: * Chest x-ray ≥ 20 mm * CT scan (with slice thickness of ≤ 5 mm) ≥ 10 mm--\>Longest diameter * Physical exam (using calipers) ≥ 10 mm * Lymph nodes by CT scan ≥ 15 mm --\>Measured in short axis * All radiology studies must be performed within 14 days prior to registration (within 21 days if negative). * Patients must have at least one additional tumour mass amenable to core needle or excisional biopsy (Note FNA is not acceptable) that is not a measurable lesion that will be used as a target lesion. Patients must consent to and be willing and able to undergo at least two core needle biopsies of that lesion. * Age ≥ 18 years * ECOG performance status of 0 or 1 * Patients must have received at least one prior standard first line regimen for advanced or metastatic disease. The regimen may have been cytotoxic chemotherapy, targeted therapy, hormonal therapy (for e.g. anastrozole) or immunotherapy providing considered a standard first line therapy. There is no limit to the number of prior regimens but investigators and their patients should carefully consider the likelihood of benefit of an immunologic therapy in heavily pretreated patients. * For phase II, patients may be enrolled prior to disease progression, provided they have completed their first line therapy as below and they have documented stable disease on two consecutive tumour assessments (i.e. do not have evidence of tumour regression from therapy): * NSCLC patients may be entered after a minimum of 4-6 cycles of first line combination chemotherapy; if the patient is \>70 years a single agent regimen is acceptable. If the patient has documented EGFR or ALK mutations, treatment they may have received may include an EGFR inhibitor or ALK inhibitor as first line therapy. * Breast cancer patients may be entered after a minimum of 6 cycles of first line therapy. * Patients with metastatic/recurrent esophageal carcinoma may be entered after first line chemotherapy for metastatic disease. * Washout period between last day of prior treatment and planned start of treatment is the longest of one of the following: * two weeks * standard cycle length of prior regimen * 10 half-lives for investigational drugs. * 30 days since last dose of ipilumumab or PR1/PDL1 therapy. * Patients must have recovered from any treatment related toxicities prior to registration (unless grade 1, irreversible and considered not clinically significant). Progression must be documented post radiotherapy if was given to the only site of measurable disease. * Patients may have had prior radiation therapy. A minimum of 28 days (4 weeks) must have elapsed between the last dose of radiation and date of registration (14 days for a single palliative fraction of radiation to a non-target lesion). Patients must have recovered from any acute toxic effects from radiation prior to registration (unless grade 1, irreversible and considered not clinically significant). * Previous surgery is permitted. A minimum of 28 days (4 weeks) must have elapsed between any major surgery and date of registration (7 days for minor surgery), provided that wound healing has occurred. * Laboratory requirements done within 7 days prior to registration: * WBC ≥ 3.0 x 10\^9/L * absolute neutrophils ≥ 1.5 x 10\^9/L * platelets ≥ 75 x 10\^9/L * INR ≤ 1.2 * bilirubin ≤ 1.5 x UNL (upper normal limit) * AST and ALT ≤ 3.0 x UNL or ≤ 5.0 x UNL if patient has liver metastases * serum creatinine ≤ 1.5 x UNL or creatinine clearance ≥ 60ml/min * serum phosphate \> 0.8mMol/L (grade 0-1) * Patient consent must be appropriately obtained in accordance with applicable local and regulatory requirements. Each patient must sign a consent form prior to registration and prior to tests which are considered to be study specific * Patients who cannot give informed consent (i.e. mentally incompetent patients, or those physically incapacitated such as comatose patients) are not to be recruited into the study. Patients competent but physically unable to sign the consent form may have the document signed by their nearest relative or legal guardian. Each patient will be provided with a full explanation of the study before consent is requested. * Patients must be accessible for treatment and follow up. Patients registered on this trial must be treated and followed at the participating centre. * Pre-treatment biopsy must be done within 5 working days after registration and treatment is to begin within 5 working days of the pre-treatment biopsy (max. 10 working days from registration). Exclusion Criteria: * Patients with a history of other active or current malignancies that require active treatment * Patients with known symptomatic brain metastases. Patients with treated and radiologic or clinical evidence of stable brain metastases, are eligible providing that they have been stable for at least 3 months, are asymptomatic and do not require corticosteroids (must have discontinued steroids at least 1 month prior to entry). * Patients receiving concurrent treatment with other anti-cancer therapy or other investigational agents. * Patients who have had prior treatment with AdVAC, MG1MA3 or any MAGE-A3 targeted therapy. * Pregnant or lactating women. Men and women of childbearing potential who do not agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of the study participation. * Serious illness or medical condition which would not permit the patient to be managed according to the protocol, including, but not limited to: 1. History of significant neurologic or psychiatric disorder (e.g. uncontrolled psychotic disorders) which would impair the ability to obtain consent or limit compliance with study requirements. 2. Active uncontrolled or serious infection (viral, bacterial or fungal) or a history of opportunistic infection associated with an immunodeficient state. 3. Significant immunodeficiency due to underlying illness (e.g. known HIV/AIDS) and/or medication (e.g. systemic corticosteroids). 4. Known myeloproliferative disorders requiring systemic therapy. 5. Other medical conditions that might be aggravated by study treatment. * Patients with uncontrolled pre-existing cardiovascular conditions and/or symptomatic cardiac dysfunction. * Patients with household contacts meeting any of the following criteria are ineligible for study entry unless alternate living arrangements can be made: 1. Women who are pregnant or nursing an infant 2. Children \< 12 months old 3. Anyone with significant immunodeficiency due to underlying illness (e.g. HIV/AIDS) and/or medication (e.g. systemic corticosteroids) * Use of anti-viral medication, steroids, immunosuppressive agents (cyclosporine, interferon) or immunization (including the flu shot) within 14 days prior to registration. Use of anti-viral, anti-platelet, or anti-coagulation medication that cannot be discontinued within 14 days of enrollment. * Patients with disease/tumour invading a major vascular structure (e.g. carotid artery), tumour related impending bowel obstruction or clinically significant and/or rapidly accumulating ascites, pericardial or pleural effusions. * Patients with conditions likely to have resulted in splenic dysfunction (e.g. splenectomy, sickle cell anemia, radiation to the spleen ≥ 20Gy, congenital asplenism). * Patients with ≥ grade 2 dyspnea and/or requirement for supplemental oxygen. Patients with important pulmonary disease must complete a 6 minute ambulation test with O2 states ≥ 90% to be eligible