Personalized Neoantigen Peptide-Based Vaccine in Combination With Pembrolizumab for Treatment of Advanced Solid Tumors

Inclusion Criteria COHORT 1 and COHORT 2 are no longer enrolling. PHASE I PRE-REGISTRATION, ALL: * Willing to provide tissue specimens per protocol * NOTE: includes fresh tissue specimen at pre-registration for complete exome and transcriptome sequencing. Patients who had tumor sequencing under certain Mayo Institutional Review Board (IRB) protocols and neoantigen has been identified or REAL Neo vaccine produced are allowed to proceed to pre-registration and/or registration. * Measurable disease as defined by RECIST (version 1.1) criteria or non-measurable disease * NOTE: Tumor lesions in previously irradiated area are not considered measurable disease * Patients with actionable genomic abnormality including, but not limited to EGFR, ALK, MET, ROS-1, RET, NTRK, KRAS or BRAF must have received and progressed on at least one line of prior FDA-approved targeted therapy * Provide written informed consent * Willing to return to enrolling institution for follow-up * Willing to provide blood specimens for research * Negative pregnancy test =\< 7 days prior to pre-registration for persons of childbearing potential. If urine test cannot be confirmed negative, serum pregnancy test will be required. * Willing to employ highly effective method of contraception from pre-registration through 6 months after final vaccine cycle * Willing to receive tetanus vaccination if subject has not had one =\< 1 year prior to pre-registration * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) of 0 or 1 * Anticipated life expectancy \> 6 months * Recovered from all toxicities associated with prior treatment to acceptable baseline status (see specified inclusion limits for laboratory toxicity) or National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 Grade 0 or 1, except for toxicities not considered safety risk per treating investigator (e.g., alopecia or vitiligo). * The following lab values obtained =\< 28 days prior to pre-registration: * Hemoglobin \>= 9.0 g/dL (Must be \>= 7 days after most recent transfusion) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 or \>= 1.5 X 10\^9/L * Platelet count \>= 100,000/mm\^3 or \>= 100 X 10\^9/L (Must be \>=7 days after most recent transfusion) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate transaminase (AST) and alanine transaminase (ALT) =\< 3 x ULN or =\< 5 x ULN with liver metastases * Creatinine =\< 1.5 x ULN OR calculated creatinine clearance must be \>= 50 ml/min using Cockcroft-Gault formula * International normalized ratio (INR) or prothrombin time (PT) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless patient is receiving anticoagulant therapy in which case PT or PTT must be within target range of therapy PHASE I REGISTRATION, ALL: * Successful sequencing and production of REAL-Neo vaccine * Measurable disease as defined by RECIST (version 1.1) criteria or non-measurable disease * NOTE: Tumor lesions in previously irradiated area are not considered measurable disease * ECOG PS 0 or 1 * Anticipated life expectancy \> 6 months * The following lab values obtained =\< 14 days prior to registration: * Hemoglobin \>= 9.0 g/dl * ANC \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 x ULN * ALT and AST =\< 3 x ULN (=\< 5 x ULN with liver involvement) * PT/INR and aPTT =\< 1.5 x ULN unless patient is receiving anticoagulant therapy in which case INR or aPTT must be within target range of therapy * Calculated creatinine clearance \>= 50 ml/min using Cockcroft-Gault formula * Provide written informed consent * Willing to provide blood and tissue specimens for research * Willing to return to enrolling institution for follow-up * Patients with actionable genomic abnormality including, but not limited to EGFR, ALK, MET, ROS-1, RET, NTRK, KRAS or BRAF must have also received and progressed on at least one line of prior FDA-approved targeted therapy * Negative pregnancy test =\< 14 days prior to registration for persons of childbearing potential only * NOTE: If urine test cannot be confirmed negative, serum pregnancy test will be required * Willing to employ highly effective method of contraception from pre-registration through 6 months after final vaccine cycle * Willing to receive tetanus vaccination if subject has not had one =\< 1 year prior to pre-registration * Recovered from all toxicities associated with prior treatment to acceptable baseline status (for laboratory toxicity see specified limits for inclusion) or NCI CTCAE version 5.0 Grade of 0 or 1, except for toxicities not considered safety risk per treating investigator (e.g., alopecia or vitiligo) PHASE II PRE-SCREENING COHORT 3 ONLY: * ECOG PS 0 or 1 * Histological confirmation of adenocarcinoma of the breast with estrogen receptor (ER) \< 10%, progesterone receptor (PR) \< 10%, and HER2 negative based on current American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guideline * Stage I-III based on 7th edition of TNM staging system from American Joint Committee on Cancer (AJCC) * Evidence of residual disease \>= 1 cm after neoadjuvant pembrolizumab-based chemotherapy on imaging for patients who have not had surgery * Willing to proceed with surgery and provide tissue and blood specimens for patients who have not had surgery * Provide written informed consent * Willing to return to enrolling institution for follow-up PHASE II PRE-SCREENING COHORT 4 ONLY: * ECOG PS 0 or 1 * Histological confirmation of lung NSCLC * No actionable EGFR mutations and ALK fusions * Stage II or stage III based on AJCC 8th * Tumor \>= 2 cm on pre-surgery evaluation imaging (residual disease \>= 2 cm after neoadjuvant therapy on pre-surgery evaluation imaging in patient who receives neoadjuvant therapy) for patients who have not had surgery. Patients with or without neoadjuvant chemotherapy or immunotherapy are allowed * Provide written informed consent * Willing to proceed with surgery and provide tissue and blood specimens for patients who have not had surgery * Willing to return to enrolling institution for follow-up PHASE II PRE-REGISTRATION COHORT 3 (TNBC) ONLY: * Histologically confirmed residual cancer burden 2 and 3 in surgical specimens PHASE II PRE-REGISTRATION COHORT 4 (NSCLC) ONLY: * Tumor without complete pathologic response is confirmed in pathology * Willing to proceed with surgery and provide tissue specimens for complete exome and transcriptome sequencing * NOTE: Patients who had sequencing under certain Mayo IRB protocols and neoantigens identified or REAL Neo vaccine produced are allowed to proceed to pre-registration and/or registration * Negative pregnancy test ≤7 days prior to pre-registration for persons of childbearing potential only. If urine test cannot be confirmed negative, serum pregnancy test will be required. * Willing to employ highly effective method of contraception from pre-registration through 6 months after final vaccine cycle * ECOG PS of 0 or 1 * Anticipated life expectancy \> 6 months PHASE II REGISTRATION: * Successful sequencing and production of REAL-Neo vaccine * Patients will receive \>= 2 additional cycles of maintenance pembrolizumab * ECOG PS 0 or 1 * Anticipated life expectancy \> 6 months * The following lab values obtained =\< 14 days prior to registration: * Hemoglobin \>= 9.0 g/dl * ANC \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 x ULN * ALT and AST =\< 3 x ULN (=\< 5 x ULN with liver involvement) * PT/INR and aPTT =\< 1.5 x ULN unless patient is receiving anticoagulant therapy in which case INR or aPTT must be within target range of therapy * Calculated creatinine clearance \>= 50 ml/min using Cockcroft-Gault formula * Provide written informed consent * Willing to provide blood specimens for research * Willing to return to enrolling institution for follow-up * Negative pregnancy test =\< 14 days prior to registration for persons of childbearing potential only. If urine test cannot be confirmed negative, serum pregnancy test will be required. * Willing to employ highly effective method of contraception from pre-registration through 6 months after final vaccine cycle * Willing to receive tetanus vaccination if subject has not had one =\< 1 year prior registration * Recovered from all toxicities associated with prior treatment to acceptable baseline status NCI CTCAE version 5.0 Grade of 0 or 1, except for toxicities not considered safety risk per treating investigator (e.g., alopecia or vitiligo) Exclusion Criteria ALL PHASES: * Any of the following because study involves investigational agent whose genotoxic, mutagenic and teratogenic effects on developing fetus and newborn are unknown: * Pregnant person * Nursing person unwilling to stop breast feeding * Person of childbearing potential unwilling to employ adequate contraception from registration through 6 months after final vaccine cycle * Co-morbid systemic illnesses or other severe concurrent disease which, in judgment of investigator, would make patient inappropriate for entry into this study or interfere significantly with proper assessment of safety and toxicity of prescribed regimens * History of myocardial infarction =\< 6 months prior to pre-registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias. * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy PHASE I PRE-REGISTRATION: * Acute, reversible effect(s) of prior therapy not recovered to baseline regardless of interval since last treatment * Uncontrolled illness including, but not limited to: * Ongoing or active infection * Psychiatric illness/social situations * Congestive heart failure with New York Heart Association (NYHA) class III or IV moderate to severe objective evidence of cardiovascular disease * Stroke =\< 3 months prior to pre-registration * Significant cardiac arrhythmia or unstable angina * Any other conditions that would limit compliance with study requirements * Receiving any other investigational agent which would be considered treatment for primary neoplasm, except pembrolizumab * Any prior hypersensitivity or adverse reaction to GM-CSF * Other active malignancy =\< 3 years prior to pre-registration * EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix * NOTE: If there is history of prior malignancy, they must not be receiving other specific treatment for their cancer * History of active autoimmune disease (AD) that required systemic treatment in =\< 30 days (i.e., use of disease modifying agents, corticosteroids \> 10 mg daily prednisone equivalent, or other immunosuppressive drugs) prior to pre-registration * NOTE: Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered systemic treatment. Patients with vitiligo, Graves disease, or psoriasis not requiring systemic treatment within the past 30 days are not excluded. Patients with celiac disease controlled with diet modification are not excluded PHASE I REGISTRATION * Any of the following prior therapies: * Chemotherapy, experimental drugs (except pembrolizumab), or small molecules inhibitors (except for endocrine therapies) =\< 3 weeks prior to registration * Radiation =\< 2 weeks prior to registration * Major Surgery =\< 4 weeks prior to registration * Received live vaccine =\< 30 days prior to registration * Palliative radiation therapy for symptoms control including, but not limited to, bone metastatic lesion radiation therapy is allowed, but last dose of radiation therapy should be \> 14 days from first dose of vaccination on study * CTCAE \>= Grade 3 treatment-emergent adverse event (TEAE) to prior checkpoint inhibitor, TEAE requiring systemic corticosteroids (\> 10 mg daily prednisone equivalent), or permanent treatment discontinuation due to toxicity * Neuromuscular disorders (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis and spinal muscular atrophy) or history of rhabdomyolysis * Active ADs that require chronic systemic steroids (\> 10 mg daily prednisone equivalent) or immunosuppressive agents * Systemic corticosteroids (\> 10 mg daily prednisone equivalent) or other immunosuppressive medications =\< 14 days prior to registration * NOTE: Inhaled or topical steroids and adrenal replacement steroid doses \> 10 mg daily prednisone equivalent permitted in absence of active AD * Evidence of leptomeningeal disease or central nervous system metastases that are untreated, symptomatic, or require steroids \>10 mg daily prednisone equivalent * NOTE: Patients with history of stable treated brain metastases are eligible. Stable treated metastases defined as no evidence of progression for ≥4 weeks on brain imaging (MRI or CT scan) PHASE II PRE-SCREENING: * Uncontrolled illness including, but not limited to: * Ongoing or active infection * Congestive heart failure with NYHA class III or IV; moderate to severe objective evidence of cardiovascular disease * Significant cardiac arrhythmia or unstable angina * Any other conditions that would limit compliance with study requirements * Any prior hypersensitivity or adverse reaction to GM-CSF * Other active malignancy =\< 3 years prior to pre-screening * EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix * NOTE: If there is history of prior malignancy, they must not be receiving other specific treatment for their cancer * Known history of active AD that has required systemic treatment in the =\< 30 days (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs) prior to pre-screening * NOTE: Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered systemic treatment. Patients with vitiligo, Graves' disease, or psoriasis not requiring systemic treatment within the past 30 days are not excluded. Patients with Celiac disease controlled with diet modification are not excluded. PHASE II PRE-REGISTRATION * Uncontrolled illness including, but not limited to: * Congestive heart failure with NYHA class III or IV; moderate to severe objective evidence of cardiovascular disease * Significant cardiac arrhythmia or unstable angina * Any other conditions that would limit compliance with study requirements * Any prior hypersensitivity or adverse reaction to GM-CSF * Other active malignancy =\< 3 years prior to pre-registration * EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix * NOTE: If history of prior malignancy, must not be receiving other specific treatment for cancer * Known history of active AD that has required systemic treatment in the =\< 30 days (i.e., with use of disease modifying agents, corticosteroids \> 10 mg daily prednisone equivalent, or other immunosuppressive drugs) prior to pre-registration * NOTE: Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid therapy for adrenal or pituitary insufficiency) is not considered systemic treatment. Patients with vitiligo, Graves' disease, or psoriasis not requiring systemic treatment within the past 30 days are not excluded. Patients with Celiac disease controlled with diet modification are not excluded. * Patients will also be excluded based on tissue/ribonucleic acid (RNA)/deoxyribonucleic acid (DNA) quality and quantity. If any of the following quality and quantity thresholds are not met, patient will be excluded: (1) tumor tissue cellularity equal to or greater than 30%; (2) there are \>= 2 cores with passing cellularity; (3) \>= 30% of tumor RNA with fragment sizes are \>= 200 base pairs (DV200 \>= 30); (4) \< 10% of DNA fragments are smaller than 1 kb; and (5) sufficient amount of both DNA (blood and tumor) and RNA (tumor) for exome sequencing and whole transcriptome sequencing (RNAseq) according to Mayo sequencing core. (Kits and technologies change overtime, so these are not fixed numbers.) PHASE II REGISTRATION * Evidence of metastatic disease or recurrence * Any of the following prior therapies: * Chemotherapy, experimental drugs (except pembrolizumab), or small molecules inhibitors (except for endocrine therapies) =\< 3 weeks prior to registration * Radiation =\< 2 weeks prior to registration * Major surgery =\< 4 weeks prior to registration * Received live vaccine =\< 30 days prior to registration * NOTE: Continuation of pembrolizumab per standard of care is allowed * NOTE: Palliative radiation therapy for symptoms control including, but not limited to, bone metastatic lesion radiation therapy is allowed, but last dose of radiation therapy should be \> 14 days from first dose of vaccination on study * CTCAE \>= grade 3 TEAE to prior checkpoint inhibitor, TEAE requiring systemic corticosteroids (\> 10 mg daily prednisone equivalent), or permanent treatment discontinuation due to toxicity * Neuromuscular disorders (e.g., inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis and spinal muscular atrophy), or history of rhabdomyolysis * Active ADs that require chronic systemic steroids (\> 10 mg daily prednisone equivalent) or immunosuppressive agents * Requirement for systemic corticosteroids (\> 10 mg daily prednisone equivalent) or other immunosuppressive medications =\< 14 days prior to registration * NOTE: Inhaled or topical steroids and adrenal replacement steroid doses \> 10 mg daily prednisone equivalent are permitted in