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

Inclusion Criteria: * PRE-REGISTRATION COHORT 1 ONLY: Histologically confirmed unresectable locally advanced or metastatic solid malignancies * PRE-REGISTRATION COHORT 1 ONLY: Has cancer progression after at least one line of standard of care systemic treatment * PRE-REGISTRATION COHORT 2 ONLY: Histologically confirmed unresectable locally advanced or metastatic solid malignancies that pembrolizumab is Food and Drug Administration (FDA) approved indication including melanoma, non-small cell lung cancer (NSCLC), head and neck squamous cell cancer (HSNCC), urothelial carcinoma, any microsatellite instability (MSI)-high tumor, gastric or gastroesophageal junction (GEJ) adenocarcinoma, cervical cancer, hepatocellular carcinoma (HCC), merkel cell carcinoma (MCC), renal cell carcinoma (RCC), endometrial carcinoma, tumor mutational burden-high (TMB-H) cancer, cutaneous squamous cell carcinoma (cSCC), and triple-negative breast cancer (TNBC) or other solid tumors that will benefit from pembrolizumab per the treating physician's judgment. * PRE-REGISTRATION COHORT 2 ONLY: Patient is eligible to receive pembrolizumab with or without chemotherapy per the treating physician's judgement or has been on pembrolizumab through compassionate use * PRE-REGISTRATION: Age \>= 18 years * PRE-REGISTRATION: Willing to provide mandatory tissue specimens per protocol * NOTE: This includes mandatory fresh tissue specimen at pre-registration for complete exome and transcriptome sequencing unless patient had sequencing under Mayo Institutional Review Board (IRB) protocol #13-000942, #14-004094, or #21-007742 and has been identified for potential production of REAL Neo vaccine. Patients who had sequencing under Mayo IRB protocol #13-000942, #14-004094, or #21-007742 and have been identified for potential production of REAL Neo vaccine are allowed to proceed with neoantigen production. * PRE-REGISTRATION: Measurable disease as defined by RECIST (version 1.1) criteria * NOTE: Tumor lesions in a previously irradiated area are not considered measurable disease or non-measurable disease * PRE-REGISTRATION: 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 * PRE-REGISTRATION: Provide written informed consent * PRE-REGISTRATION: Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) * PRE-REGISTRATION: Willing to provide mandatory blood specimens for correlative research * PRE-REGISTRATION: Negative pregnancy test done =\< 7 days prior to pre-registration for persons of childbearing potential only * NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * PRE-REGISTRATION: Willing to employ a highly effective method of contraception from the time of pre-registration through 6 months after the final vaccine cycle * PRE-REGISTRATION: Willing to receive a tetanus vaccination if subject has not had one =\< 1 year prior to pre-registration * PRE-REGISTRATION: Eastern Cooperative Oncology Group (ECOG) of 0 or 1 * PRE-REGISTRATION: Anticipated life expectancy of \> 6 months * PRE-REGISTRATION: Recovered from all toxicities associated with prior treatment to acceptable baseline status (for laboratory toxicity see below limits for inclusion) or National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE), version 5.0, Grade of 0 or 1, except for toxicities not considered a safety risk per treating investigator (e.g., alopecia or vitiligo). * PRE-REGISTRATION: Hemoglobin \>= 9.0 g/dL (obtained =\< 28 days prior to pre-registration) (Must be \>= 7 days after most recent transfusion) * PRE-REGISTRATION: Absolute neutrophil count (ANC) \>= 1500/mm\^3 or \>= 1.5 X 10\^9/L (obtained =\< 28 days prior to pre-registration) * PRE-REGISTRATION: Platelet count \>= 100,000/mm\^3 or \>= 100 X 10\^9/L (obtained =\< 28 days prior to pre-registration) (Must be \>=7 days after most recent transfusion) * PRE-REGISTRATION: Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 28 days prior to pre-registration) * PRE-REGISTRATION: Aspartate transaminase (AST) and alanine transaminase (ALT) =\< 3 x ULN or =\< 5 x ULN for patients with liver metastases (obtained =\< 28 days prior to pre-registration) * PRE-REGISTRATION: Creatinine =\< 1.5 x ULN OR calculated creatinine clearance must be \>= 50 ml/min using the Cockcroft-Gault formula (obtained =\< 28 days prior to pre-registration) * PRE-REGISTRATION: 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 (obtained =\< 28 days prior to pre-registration) * REGISTRATION COHORT 1 ONLY: Histologically confirmed unresectable locally advanced or metastatic solid malignancies * REGISTRATION COHORT 1 ONLY: Has cancer progression after at least one line of standard of care systemic treatment * REGISTRATION COHORT 2 ONLY: Histologically confirmed unresectable locally advanced or metastatic solid malignancies that pembrolizumab is FDA approved indication (including melanoma, non-small cell lung cancer (NSCLC), head and neck squamous cell cancer (HSNCC), urothelial carcinoma, any microsatellite instability (MSI)-high tumor, gastric or gastroesophageal junction (GEJ) adenocarcinoma, cervical cancer, hepatocellular carcinoma (HCC), merkel cell carcinoma (MCC), renal cell carcinoma (RCC), endometrial carcinoma, tumor mutational burden-high (TMB-H) cancer, cutaneous squamous cell carcinoma (cSCC), and triple-negative breast cancer (TNBC) or other solid tumors that will benefit from pembrolizumab per the treating physician's judgement. * REGISTRATION COHORT 2 ONLY: Pembrolizumab without chemotherapy remains as a reasonable treatment option at the treating physician's decision * REGISTRATION: Age \>= 18 years * REGISTRATION: Soft tissue lesion amenable for adequate tissue sampling * NOTE: It should not be tumor which was radiated in the past. * REGISTRATION: Successful sequencing and production of REAL-Neo vaccine * REGISTRATION: Measurable disease as defined by RECIST (version 1.1) criteria * NOTE: Tumor lesions in a previously irradiated area are not considered measurable disease or non-measurable disease * REGISTRATION: ECOG Performance Status (PS) 0 or 1 * REGISTRATION: Anticipated life expectancy of \> 6 months * REGISTRATION: Hemoglobin \>= 9.0 g/dl (obtained =\< 14 days prior to registration) * REGISTRATION: Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 14 days prior to registration) * REGISTRATION: Platelet count \>= 100,000/mm\^3 (obtained =\< 14 days prior to registration) * REGISTRATION: Total bilirubin =\< 1.5 x ULN (obtained =\< 14 days prior to registration) * REGISTRATION: Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3 x ULN (=\< 5 x ULN for patients with liver involvement) (obtained =\< 14 days prior to registration) * REGISTRATION: 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 (obtained =\< 14 days prior to registration) * REGISTRATION: Calculated creatinine clearance \>= 50 ml/min using the Cockcroft-Gault formula (obtained =\< 14 days prior to registration) * REGISTRATION: Provide written informed consent * REGISTRATION: Willing to provide mandatory blood specimens for correlative research * REGISTRATION: Willing to provide mandatory tissue specimens for correlative research * REGISTRATION: Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) * REGISTRATION: 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 * REGISTRATION: Negative pregnancy test done =\< 14 days prior to registration for persons of childbearing potential only * NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * REGISTRATION: Willing to employ a highly effective method of contraception from the time of pre-registration through 6 months after the final vaccine cycle * REGISTRATION: Willing to receive a tetanus vaccination if subject has not had one =\< 1 year prior to pre-registration * REGISTRATION: Recovered from all toxicities associated with prior treatment to acceptable baseline status (for laboratory toxicity see below limits for inclusion) or National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE), version 5.0, Grade of 0 or 1, except for toxicities not considered a safety risk per treating investigator (e.g., alopecia or vitiligo) Exclusion Criteria: * PRE-REGISTRATION: Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant person * Nursing person unwilling to stop breast feeding * Person of childbearing potential who are unwilling to employ adequate contraception from the time of registration through 6 months after the final vaccine cycle * PRE-REGISTRATION: Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * PRE-REGISTRATION: 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. * PRE-REGISTRATION: Acute, reversible effect(s) of prior therapy not recovered to baseline regardless of interval since last treatment * PRE-REGISTRATION: Uncontrolled illness including, but not limited to: * Ongoing or active infection * Psychiatric illness/social situations * Congestive heart failure with New York Heart Association 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 * PRE-REGISTRATION: Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy * PRE-REGISTRATION: Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm, except for pembrolizumab * PRE-REGISTRATION: Any prior hypersensitivity or adverse reaction to GM-CSF * PRE-REGISTRATION: 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 a history of prior malignancy, they must not be receiving other specific treatment for their cancer * PRE-REGISTRATION: Known history of active autoimmune disease 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 replacement therapy for adrenal or pituitary insufficiency) is not considered a form of 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 * REGISTRATION: Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant persons * Nursing persons * Persons of childbearing potential who are unwilling to employ adequate contraception * REGISTRATION: Any of the following prior therapies: * Chemotherapy, experimental drugs (except for 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 a live vaccine =\< 30 days prior to registration * NOTE: Recent anti-PD1 or anti-PD-L1, such as pembrolizumab, nivolumab, atezolizumab, and durvalumab, is allowed, but the last dose of anti-PD-1 or anti-PD-L1 treatment should be more than 21 days from first dose of vaccination on the study (for Cohort 2 only) * Palliative radiation therapy for symptoms control including, but not limited to, bone metastatic lesion radiation therapy is allowed, but the last dose of radiation therapy should be more than 14 days from the first dose of vaccination on the study * REGISTRATION: 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 * REGISTRATION: Neuromuscular disorders (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis and spinal muscular atrophy), or a history of rhabdomyolysis * REGISTRATION: Active autoimmune diseases that require chronic systemic steroids (\> 10 mg daily prednisone equivalent) or immunosuppressive agents * REGISTRATION: 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 the absence of active autoimmune disease * REGISTRATION: Evidence of leptomeningeal disease * REGISTRATION: 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 are defined as follows: No evidence of progression for \>= 4 weeks on brain imaging (either magnetic resonance imaging \[MRI\] or computed tomography \[CT\] scan) * REGISTRATION: Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens