Inclusion Criteria:  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 (computed tomography [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 saturate oxygen (SaO2) >= 92% on ambient air. If positron emission tomography (PFT)s 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 multi-gated acquisition scan (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 Research Center (FHCRC)/Seattle Cancer Care Alliance (SCCA)/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:  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 A confirmatory scan performed at least 4 weeks after disease persistence/progression is required  BREAST CANCER SPECIFIC: Tissue confirmation of 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 disease as documented by a local laboratory with HER2-negativity defined as:  Immunohistochemistry score 0/1+ or Negative by in situ hybridization (fluorescence in situ hybridization [FISH]/chromogenic in situ hybridization [CISH]/silver-enhanced in situ hybridization [SISH]) per NCCN clinical practice guidelines in oncology for breast cancer to interpret in-situ hybridization (FISH/CISH/SISH) results for HER2 status. Confirmation of diagnosis must be or have been performed by internal pathology review of archival, initial or subsequent biopsy or other pathologic material at FHCRC/SCCA/UWMC BREAST CANCER SPECIFIC: Patients must have received stage specific standard of care therapy per NCCN guidelines and have persistent/recurrent disease after at least one line of therapy prior to enrollment on the study  Exclusion Criteria:  Fertile male patients and female patients of childbearing potential who are unwilling or unable to use 2 highly effective methods of contraception as outlined in this protocol for the duration of the study and for at least 5 months after the last dose of investigational product Any history of an immune-related Grade 4 adverse event attributed to prior cancer immunotherapy CIT (other than endocrinopathy managed with replacement therapy or asymptomatic elevation of serum amylase or lipase) Any history of an immune-related grade 3 adverse event attributed to prior CIT that required permanent discontinuation of the prior immunotherapeutic agent Immune-related adverse events related to prior CIT (other than endocrinopathy managed with replacement therapy or stable vitiligo) that have not resolved to baseline. Patients treated with corticosteroids for immune-related adverse events must demonstrate absence of related symptoms or signs for >= 4 weeks following discontinuation of corticosteroids Uncontrolled tumor-related pain. Patients requiring narcotic pain medication must be on a stable regimen at study entry. Symptomatic lesions amenable to palliative radiotherapy (e.g., bone metastases or metastases causing nerve impingement) should be treated > 4 weeks prior to enrollment. Patients should be recovered from the effects of radiation Uncontrolled pleural effusion, pericardial effusion, or ascites requiring repeated drainage more than once every 28 days. Indwelling drainage catheters (e.g., PleurX) are allowed Patients with known symptomatic brain metastases. Patients with previously diagnosed brain metastases are eligible if they have completed their treatment and have recovered from the acute effects of radiation therapy or surgery prior to study entry, have discontinued corticosteroid treatment for these metastases for at least 4 weeks and are neurologically stable for >= 1 months (confirmed by magnetic resonance imaging [MRI]) Patients with rapidly progressing disease, symptomatic visceral disease, or patients who are expected to have rapidly progressive disease over the course of several months despite bridging therapy approved by the protocol Known primary immunodeficiencies, either cellular (e.g., DiGeorge syndrome, T-negative severe combined immunodeficiency [SCID]) or combined T- and B-cell immunodeficiencies (e.g., T- and B-negative SCID, Wiskott-Aldrich syndrome, ataxia telangiectasia, common variable immunodeficiency) Prior allogeneic bone marrow transplantation or prior solid organ transplantation Positive test for human immunodeficiency virus (HIV) infection Patients with active infection causing fever (temperature > 38.1 degree Celsius [C]) or subjects with unexplained fever (temperature > 38.1C) may not receive the investigational product unless the fever is =< 38.1 for 5 days prior to start Active uncontrolled infection: individuals with a history of hepatitis C who have successfully completed antiviral therapy with an undetectable viral load, and those with hepatitis B who have, per standard practice, hepatitis well-controlled on medication (e.g., AST and ALT < 5 x ULN) can be included History of autoimmune disease that has not been controlled with treatment in the last 12 months, including, but not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener granulomatosis, Sjogren syndrome, Guillain-Barre syndrome, multiple sclerosis, vasculitis, or glomerulonephritis with the following exceptions: Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible. Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible. Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., no psoriatic arthritis) may be eligible Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone >= 10 mg/day or equivalent, cyclophosphamide, azathioprine, methotrexate, thalidomide, and TNF-alpha antagonists) within 2 weeks prior screening. The use of topical, eye drops, local injections, or inhaled corticosteroids (e.g. fluticasone for chronic obstructive pulmonary disease) is allowed. The use of oral mineralocorticoids (e.g. fludrocortisone for patients with orthostatic hypotension) is allowed. Physiologic doses of corticosteroids for adrenal insufficiency are allowed. Low dose corticosteroids for a short duration [5 mg once daily (QD) prednisone for 2 weeks] as symptomatic treatment and upon with discussion with the investigator is allowed. Note: Patients with adrenal insufficiency may take 5 mg of prednisone or equivalent daily Subjects should have an international normalized ratio (INR) or activated partial thromboplastin time (aPTT) =< 1.5 X ULN unless the subject is receiving anticoagulant therapy. Subjects on anticoagulant therapy should have a prothrombin time (PT) or partial thromboplastin time (PTT) within therapeutic range of intended use and no history of severe hemorrhage. Patients who require therapeutic anticoagulation and cannot discontinue anticoagulation safely during the day prior, day of, and day after injection are excluded. Patients requiring anticoagulation with warfarin are excluded unless they can be transitioned to an alternative anticoagulant (e.g., low molecular weight heparin or direct oral anticoagulants) prior to enrollment. Antiplatelet agents (e.g., aspirin, clopidogrel, etc.) are not considered anticoagulants for the purposes of this study (i.e., they are allowed) Other medical, social, or psychiatric factor that interferes with medical appropriateness and/or ability to comply with study, as determined by the principal investigator (PI) Participants of childbearing potential must have a negative serum pregnancy test within 14 days prior to enrollment. Childbearing potential is defined as women who have not been surgically sterilized and who are not post-menopausal (free of menses for at least 1 year) Female patients who are lactating or intend to breastfeed during the duration of the study Patients who have received a live vaccine within 30 days prior to enrollment Patients with any underlying medical condition for which, in the investigator's opinion, participation would not be in the best interest of the participant (e.g.- compromises the health of the subject) or that could prevent, limit or confound protocol assessments MELANOMA SPECIFIC: Uveal or Choroidal melanoma. This entity is excluded due to the absence of abundant mutations BREAST SPECIFIC: Patients with symptomatic disease including patients with symptomatic lung metastases, bone marrow replacement with associated cytopenia, or significant liver metastases with associated liver dysfunction