• Female and/or male patients age \>= 18 years

• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2

• Patients must have at least 1 lesion (or aggregate lesions) to obtain tumor tissue for resection of \>= 1 cm or \>= 4 core biopsies acceptable. Amenable to image (CT, ultrasound \[U/S\], or magnetic resonance imaging \[MRI\]) guided biopsy for tissue collection necessary for neoantigen identification. Either primary or metastatic sites are options for tissue collection

• Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria: Participants must have measurable disease, defined as at least one target lesion that can be measured in at least one dimension (longest diameter to be recorded) as \>= 10 mm, unless lymph node in which case short axis must be \>= 15 mm. Baseline imaging (for example diagnostic CT chest/abdomen/pelvis, PET CT scan and imaging of the affected extremity as appropriate), brain imaging (MRI or CT scan) must be obtained within 45 days of prior to start of first planned vaccine dose infusion. MRI can be substituted for CT in patients unable to have CT contrast

• Serum creatine \< 1.5 mg/dL or estimated glomerular filtration rate (eGFR) \> 60 mL/min

• Total bilirubin (tBili) \< 1.5 x upper limit of normal (ULN) and an aspartate aminotransferase (AST)/alanine aminotransferase (ALT) \< 2.5 x ULN and \< 5 x ULN for subjects with documented liver metastasis. Patients with suspected Gilbert syndrome may be included if tBili \> 3 but no other evidence of hepatic dysfunction

• =\< grade 1 dyspnea and arterial oxygen saturation (SaO2) \>= 92% on ambient air. If pulmonary function tests (PFTs) are performed based on the clinical judgement of the treating physician, patients with forced expiratory volume in 1 second (FEVI) \>= 70% of predicted and carbon monoxide diffusing capability (DLCO) (corrected) of \>= 60% of predicted will be eligible

• Patients with active interstitial lung disease (ILD)/pneumonitis or a history of ILD/pneumonitis requiring treatment with systemic steroids will be excluded

• Patients 60 years of age or older are required to have left ventricular ejection fraction (LVEF) evaluation performed within 60 days prior to enrollment. LVEF may be established with echocardiogram or MUGA scan, and left ejection fraction must be \>= 50%. Cardiac evaluation for other patients is at the discretion of the treating physician

• Subjects with a history of myocarditis or congestive heart failure (as defined by New York Heart Association functional classification III or IV), as well as unstable angina, serious uncontrolled cardiac arrhythmia, uncontrolled infection, or myocardial infarction 6 months prior to study entry will be excluded

• Absolute neutrophil count (ANC) \> 1000 cells/mm\^3

• Hemoglobin \>= 9 mg/dL

• Platelet count \>= 50,000/uL

• Toxicity from prior therapy must be recovered to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version (v.)5 grade 2 or less

• Willing and able to comply with scheduled visits, treatment plan, laboratory tests, and other procedures

• Capable of understanding and providing a written informed consent

• The effects of neoantigen vaccination on the developing human fetus are unknown. For this reason, patients who are having sex that can lead to pregnancy must agree to use adequate contraception (hormonal, barrier method of birth control, or abstinence) for the duration of study participation. Should a woman become pregnant while participating in the study, she should inform her study doctor immediately and will not receive any more study treatment

• MELANOMA SPECIFIC: Tissue confirmation of melanoma: Histologically confirmed metastatic (recurrent or de novo stage IV) or unresectable locally advanced (stage IIIC or IIID) cutaneous, acral, conjunctival or mucosal melanoma, as defined by the American Joint Committee on Cancer (AJCC) v8.0. Confirmation of diagnosis must be or have been performed by internal pathology review of archival, initial or subsequent biopsy or other pathologic material at Fred Hutchinson Cancer Center (FHCC)/University of Washington Medical Center (UWMC)

• MELANOMA SPECIFIC: Patients must have received stage specific standard of care therapy per National Comprehensive Cancer Network (NCCN) guidelines and have persistent/recurrent disease after at least one line of therapy prior to enrollment on the study

• MELANOMA SPECIFIC: Known BRAF mutational status

• MELANOMA SPECIFIC: History of detectable disease during/after treatment with a PD-1 or PD-L1 inhibitor, as defined by the Society of Immunotherapy of Cancer's definition of primary or secondary resistance (Kluger and others \[et al.\], 2020):

‣ Drug exposure \>= 6 weeks and best response progressive disease (PD) or stable disease (SD) \< 6 months or

⁃ Drug exposure \>= 6 months and best response complete response (CR), partial response (PR), or SD \> 6 months

• MELANOMA SPECIFIC: A confirmatory scan performed at least 4 weeks after disease persistence/progression is required but this requirement can be waived if the judgement of the treating clinician is that the patient would be at risk of rapid or symptomatic progression in that interval. This confirmatory scan can occur during production of the vaccine after enrollment

• BREAST CANCER SPECIFIC: Tissue confirmation of stage IV (recurrent or de novo metastatic) hormone receptor (HR) positive, HER2 negative breast cancer:

‣ Hormone receptor (HR) positive breast cancer as defined by either one, or both of the following criteria:

• Estrogen receptor (ER) positive disease defined as follows documented by a local laboratory: 1-100% positive stained cells based on de novo tumor biopsy

∙ Progesterone receptor (PR) positive disease defined as follows documented by a local laboratory: 1-100% positive stained cells based on de novo tumor biopsy

⁃ Human epidermal growth factor receptor 2 (HER2) negative breast cancer (per American Society of Clinical Oncology \[ASCO\]/College of American Pathologists \[CAP\] guideline update, 2018) as documented by a local laboratory with HER2-negativity defined as:

• Immunohistochemistry score 0/1+ or 2+ and / or

∙ Negative by in situ hybridization (fluorescence in situ hybridization \[FISH\]/chromogenic in situ hybridization \[CISH\]/silver-enhanced in situ hybridization \[SISH\]) per ASCO/CAP guideline update, 2018

⁃ Confirmation of diagnosis must be or have been performed by internal pathology review of archival, initial or subsequent biopsy or other pathologic material at FHCC/UWMC

• BREAST CANCER SPECIFIC: Patients must have received at least one line of systemic therapy in the metastatic setting prior to enrollment on the study and have progressive/persistent disease after

• NON-SMALL CELL LUNG CANCER SPECIFIC: Tissue confirmation of stage III unresectable or stage IV (recurrent or de novo metastatic) non-small cell lung cancer (NSCLC):

‣ Genetic testing must have been performed for targetable driver mutations, including EGFR, ROS1, Alk, KRAS, BRAF

⁃ Confirmation of diagnosis must be or have been performed by internal pathology review of archival, initial or subsequent biopsy or other pathologic material at FHCC/UWMC

• NON-SMALL CELL LUNG CANCER SPECIFIC: Patients must have received at least one line of systemic therapy in the metastatic or stage II or III setting including a PD-1 or PD-L1 inhibitor prior to enrollment on the study and have progressive or recurrent disease after

• NON-SMALL CELL LUNG CANCER SPECIFIC: For patients who have received neoadjuvant, adjuvant, and/or consolidation anti-PD-1 or anti-PD-L1 for stage II or III disease, they must have experienced disease progression in less than or equal to 365 days from initiation (cycle 1 day 1) of anti-PD-1 or anti-PD-L1 therapy for this to count as the systemic therapy for advanced disease. Patients experiencing progression more than 365 days from initiation (cycle 1 day 1) of anti-PD-1 or anti-PD-L1 therapy will not be considered as having received one line of systemic therapy. These patients must have received an anti-PD-1 or anti-PD-L1 therapy for stage IV or recurrent disease