Multi-Targeted Recombinant Ad5 (CEA/MUC1/Brachyury) Based Immunotherapy Vaccine Regimen in People With Advanced Cancer

* INCLUSION CRITERIA: * Age greater than or equal to 18 years (male and female). * Ability to understand and provide signed informed consent that fulfills Institutional Review Board (IRB)'s guidelines. * Subjects with cytologically or histologically confirmed locally advanced or metastatic solid tumor malignancy. * Subjects must have completed or had disease progression on at least one prior line of disease-appropriate therapy or not be candidates for therapy of proven efficacy for their disease. * Subjects may have measurable or non-measurable but evaluable. Subjects with surgically resected locally advanced or metastatic disease at high risk of relapse are also eligible. * Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 1. * Subjects who have received prior carcinoembryonic antigen (CEA), mucin-1 (MUC1), and/or Brachyury-targeted immunotherapy (vaccine) are eligible for this trial if this treatment was discontinued at least 4 weeks prior to enrollment. * Resolution of clinically significant side effects of prior chemotherapy, radiotherapy, immunotherapy or surgical procedures to National Cancer Institute (NCI) Common Terminology Criteria in Adverse Events (CTCAE) Grade less than or equal to 1 or grade less than or equal to 2 for neuropathy. * Adequate hematologic function at screening, as follows: * Absolute neutrophil count (ANC) \>= 1 x 10\^9/L * Hemoglobin \>= 9 g/dL * Platelets \>= 75,000/mcL. * Adequate renal and hepatic function at screening, as follows: * Serum creatinine less than or equal to 1.5 x upper limit of normal (ULN) OR creatinine clearance (CrCl) \>= 40 mL/min (if using the Cockcroft-Gault formula below): * Female CrCl = ((140 - age in years) x weight in kg x 0.85) / (72 x serum creatinine in mg/dL) * Male CrCl = ((140 - age in years) x weight in kg x 1.00)/ 1.00) / (72 x serum creatinine in mg/dL) * Bilirubin less than or equal to 1.5 x ULN OR in subjects with Gilbert's syndrome, a total bilirubin less than or equal to 3.0 x ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) less than or equal to 2.5 x ULN, unless liver metastases are present, then values must be less than or equal to 3 x ULN) * The effects of the combination ETBX-011, ETBX-051, ETBX-061 vaccine regimen on the developing human fetus are unknown. For this reason, female subjects of childbearing potential defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy or tubal ligation) or who is not postmenopausal (menopause being defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes) and male patients who are not surgically sterile (vasectomy etc.), must agree to use acceptable contraceptive methods for the duration of the study and for one month after the last vaccination. Acceptable forms of contraception include oral contraceptives, intrauterine device, condom or vaginal diaphragm plus spermicidal (gel/foam/cream/vaginal suppository), or total abstinence. * Ability to attend required study visits and return for adequate follow up, as required by this protocol. EXCLUSION CRITERIA: * Pregnant and nursing women. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with combination ETBX-011, ETBX-051, ETBX-061, breastfeeding should be discontinued if the mother is treated with combination ETBX-011, ETBX-051, ETBX-061. These potential risks may also apply to other agents used in this study. * There should be a minimum of 4 weeks from any prior investigational drug, chemotherapy, immunotherapy, with the exception of hormonal therapy for prostate and breast cancers, human epidermal growth factor receptor 2 (HER2-) directed therapy for HER2+ breast or stomach cancer (3+ immunohistochemistry (IHC) or fluorescence in situ hybridization (FISH+), drugs targeting epidermal growth factor receptor (EGFR), anaplastic large-cell lymphoma kinase (ALK) or ROS1 in EGFR,ALK, ROS1-mutated lung cancer, respectively, or standard maintenance therapies for any solid tumor under the condition that subjects are on these therapies for at least two months before start of trial treatment. * There should also be a minimum of 4 weeks from any prior radiotherapy except for palliative bone directed therapy. * Known active brain or central nervous system metastasis (less than 1 month out from definitive radiotherapy or surgery), or seizures requiring anticonvulsant treatment, or clinically significant cerebrovascular accident or transient ischemic attack (\<3 months). * Subjects with active autoimmune disease requiring systemic immunosuppressive treatment within the past 4 weeks such as but not restricted to inflammatory bowel disease, systemic lupus erythematosus, ankylosing spondylitis, scleroderma, or multiple sclerosis. A history of autoimmune disease which is not active nor has required recent systemic immunosuppressive therapy (\< 4 weeks prior to enrollment) is not reason for exclusion. * Subjects with serious intercurrent chronic or acute illness, such as cardiac or pulmonary disease, hepatic disease, or other illness considered by the Investigator as high risk for investigational drug treatment. * Subjects with clinically significant heart disease, such as congestive heart failure (class II, III, or IV defined by the New York Heart Association functional classification), history of unstable or poorly controlled angina, or history (\< 1 year) of ventricular arrhythmia. * Subjects with a medical or psychological impediment that would impair the ability of the subject to receive therapy per protocol or impact ability to comply with the protocol or protocol-required visits and procedures. * History of second malignancy within 3 years prior to enrollment except for the following: adequately treated non-melanoma skin cancer, cervical carcinoma in situ, superficial bladder cancer or other localized malignancy after discussion with the medical monitor. * Presence of a known active acute or chronic infection, including human immunodeficiency virus (HIV, as determined by enzyme-linked immunosorbent assay (ELISA) and confirmed by western blot) and hepatitis B and hepatitis C virus (HBV/HCV, as determined by hepatitis B surface antigen (HBsAg) and hepatitis C serology). * Subjects on systemic intravenous or oral corticosteroid therapy with the exception of physiologic doses of corticosteroids (less than or equal to the equivalent of prednisone 10 mg/day) or other immunosuppressives such as azathioprine or cyclosporin A are excluded on the basis of potential immune suppression. For these subjects these excluded treatments must be discontinued at least 2 weeks prior to enrollment for recent short course use (less than or equal to 14 days) or discontinued at least 4 weeks prior to enrollment for long term use (\> 14 days). In addition, the use of corticosteroids as premedication for contrast-enhanced studies is allowed prior to enrollment and on study. * Subjects with known allergy or hypersensitivity to any component of the investigational product will be excluded. * Subjects with acute or chronic skin disorders that will interfere with injection into the skin of the extremities or subsequent assessment of potential skin reactions will be excluded. * Subjects vaccinated with a live (attenuated) vaccine (e.g., FluMist(R)) or a killed (inactivated)/subunit vaccine (e.g., PNEUMOVAX(R), Fluzone(R)) within 28 days or 14 days, respectively, of the first planned dose of ETBX vaccine.