Inclusion Criteria:

          -  Have clinically or pathologically confirmed diagnosis of unresectable and metastatic
             breast cancer with no curative treatment options

          -  Have been informed of other treatment options

          -  Patient must have lesion that can be biopsied and is willing to undergo the procedure
             as part of the protocol

          -  Have an Eastern Cooperative Oncology Group (ECOG) performance status of =< 1

          -  Participants of child-bearing potential must agree to use adequate contraceptive
             methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study
             entry. Should a woman become pregnant or suspect she is pregnant while she or her
             partner is participating in this study, she should inform her treating physician
             immediately

          -  For patients with history of radiotherapy to the same side of chest wall/breast,
             he/she will be eligible only if doses under 70 Gy total to the chest wall, if
             delivered more than 6 months prior to planned re-treatment

          -  Patients must have measurable disease per Response Evaluation Criteria in Solid Tumors
             (RECIST) 1.1 criteria, and documented available breast tumor for injections: the
             longest axis of the tumor is at least 1 cm

          -  Have measurable distant disease per RECIST 1.1 criteria present

          -  Any line of therapy allowed, radiologically or clinically confirmed progression on
             prior therapy

          -  No cancer-directed therapy for at least 3 weeks prior to study treatment
             (bone-directed therapies are allowed)

          -  Platelets >= 100,000/uL

          -  Hemoglobin >= 9.0 g/dL

          -  Absolute neutrophil count (ANC) >= 1500/uL

          -  Total bilirubin =< 1.5 X institutional upper limit of normal (ULN)

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 X
             institutional ULN

          -  Creatinine =< 1.5 X ULN OR creatinine clearance >= 50 mL/min per Cockcroft-Gault
             equation for patients with creatinine levels greater than ULN

          -  Participant or legal representative must understand the investigational nature of this
             study and sign an Independent Ethics Committee/Institutional Review Board approved
             written informed consent form prior to receiving any study related procedure

          -  Patients must agree to injections of CDX-301, CDX-1140, and poly-ICLC

          -  Patients must agree to radiation to the breast tumor

          -  Patients must agree to appropriate clinical monitoring to receive the study regimens

          -  Patients must agree to photos of tumors and use of the photos for publication

          -  Patients should have an administration site for all injections that is free of
             potentially complicating dermatologic conditions such as rashes and should not be
             located in an area where the integrity of the draining lymph node bed is potentially
             compromised (i.e., an extremity where a nodal resection was previously performed)

        Exclusion Criteria:

          -  Patients currently treated with systemic immunosuppressive agents, including steroids,
             are ineligible until 3 weeks after removal from immunosuppressive treatment. (inhaled
             steroids are allowed)

          -  Patients with active or history of autoimmune disease or history of transplantation

          -  Patients with active or prior history of non-infectious pneumonitis

          -  Patients with prior history of acute myeloid leukemia (AML) or known FLT3 aberrations

          -  Pregnant or nursing female participants

          -  Unwilling or unable to follow protocol requirements

          -  Patients with known serious mood disorders. (Major depression diagnosis is an
             exclusion: Other stable mood disorders on stable therapy for > 6 months or not
             requiring therapy may be allowed after consultation with principal investigator [PI])

          -  Cardiac risk factors including:

               -  Patients experiencing cardiac event(s) (acute coronary syndrome, myocardial
                  infarction, or ischemia) within 3 months of signing consent

               -  Patients with a New York Heart Association classification of III or IV

          -  Patients with inflammatory breast cancer

          -  Patients with uncontrolled diseases other than cancer may be excluded if after
             consultation with PI and research team it is decided it might affect the treatment
             efficacy or toxicity

          -  Evidence of current drug or alcohol abuse or psychiatric impairment, which in the
             investigator's opinion will prevent completion of the protocol therapy or follow-up.
             Specific testing is not required, however may be done as clinically indicated

          -  Any condition which in the investigator's opinion deems the participant an unsuitable
             candidate to receive study drug

          -  Participants with symptomatic known brain metastases < 4 weeks from radiation
             treatment should be excluded from this clinical trial because of their poor prognosis
             and because they often develop progressive neurologic dysfunction that would confound
             the evaluation of neurologic and other adverse events

          -  Other invasive cancers diagnosed < 3 years back that required systemic treatment. If
             diagnosed with other invasive cancer >= 3 years, should have complete recovery from
             all systemic toxicity except neuropathy and alopecia

          -  Live vaccines within 30 days prior to the first dose of trial treatment and while
             participating in the trial. Examples of live vaccines include, but are not limited to,
             the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies,
             Bacillus Calmette-Guerin (BCG), and typhoid vaccine

          -  Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)

          -  Has known active hepatitis B (e.g., hepatitis B surface antigen [HBsAg] reactive) or
             hepatitis C (e.g., hepatitis C virus [HCV] ribonucleic acid [RNA] [qualitative] is
             detected)

          -  Chemotherapy, radiation therapy, or immunotherapy within 3 weeks prior to first dosing
             of study agent. Concomitant hormonal therapies are allowed

          -  Current use of anticoagulants (warfarin, heparin, direct thrombin inhibitors) at
             therapeutic levels