Inclusion Criteria:

          -  Pathologically confirmed invasive breast adenocarcinoma with documented estrogen
             receptor (ER)/progesterone receptor (PR)/human epidermal growth factor receptor 2
             (HER2) status and radiographic evidence of distant metastatic disease.

          -  Radiographic evidence of distant metastatic disease (using 7th edition American Joint
             Committee on Cancer [AJCC] criteria) with two discrete sites of measurable disease

          -  No available standard therapy that is considered curative.

               -  NOTE: Patients with ER/PR positive, HER2 negative breast cancer must have
                  progressed through at least one prior cytotoxic regimen for advanced disease and
                  no longer be candidates for standard endocrine therapy (including combination
                  therapy that includes palbociclib or everolimus). Patients with HER2 positive
                  breast cancer irrespective of ER/PR status must have received or no longer be
                  candidates for standard HER2 directed therapy (i.e., trastuzumab, pertuzumab,
                  trastuzumab, emtansine, and lapatinib). Patients with ER/PR/HER2 negative breast
                  cancer must have progressed through at least one prior cytotoxic regimen for
                  advanced disease

          -  At least one site of recurrent/metastatic disease that measures > 1 cm in greatest
             dimension (> 2 cm for lung lesions) and is amenable to safe percutaneous intratumoral
             administration of MV-s-NAP as determined by an interventional radiologist.

               -  NOTE: In Phase I of the trial (single injection), only one lesion will be
                  injected. In Phase II of the trial (3, every 3 weeks [Q3weekly] injections), the
                  same lesion will be injected unless the interventional radiologist determines
                  that lesion is not amenable to reinjection, in which case another lesion (if
                  present and measuring > 1 cm in greatest dimension [> 2 cm for lung lesions])
                  will be injected

          -  Absolute neutrophil count (ANC) >= 1500/uL (=< 7 days prior to registration)

          -  Platelets (PLT >= 100,000/uL) (=< 7 days prior to registration)

          -  Total bilirubin =< institutional upper limit of normal (=< 7 days prior to
             registration)

          -  Aspartate aminotransferase (AST) =< 2 x upper limit of normal (ULN) (=< 7 days prior
             to registration)

          -  Creatinine =< 1.5 x ULN (=< 7 days prior to registration)

          -  Hemoglobin >= 9.0 g/dL (=< 7 days prior to registration)

          -  Negative pregnancy test done =< 7 days prior to registration (for women of
             childbearing potential only)

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

          -  Ability to provide informed written consent

          -  Willingness to return to the Mayo Clinic enrolling institution for follow-up

          -  Willingness to provide biologic samples for correlative research purposes

          -  Life expectancy >= 12 weeks

          -  Concomitant administration of a bone modifying agent (e.g., zoledronic acid or
             denosumab) for the prevention or management of skeletal related events in patients
             with bone metastases and documentation of tolerability with prior exposures

        Exclusion Criteria:

          -  Known standard therapy for the patient's disease that is potentially curative or
             definitely capable of extending life expectancy

          -  Clinical or radiographic suspicion of impending visceral crisis due to invasion or
             compression by tumor

          -  Active infection =< 5 days prior to registration

          -  History of tuberculosis or history of tuberculin skin test positivity

          -  History of other malignancy =< 5 years except for non-melanoma skin cancer or
             carcinoma in situ of the cervix

          -  Any of the following prior therapies:

               -  Chemotherapy =< 3 weeks prior to registration

               -  Immunotherapy =< 4 weeks prior to registration

               -  HER2 directed therapy =< 3 weeks prior to registration

               -  Targeted therapy =< 2 weeks prior to registration (e.g., CDK4/6 inhibitors,
                  everolimus)

               -  Investigational agent =< 4 weeks prior to registration

               -  Any viral or gene therapy prior to registration

          -  Failure to fully recover from acute, reversible effects of prior systemic therapy
             regardless of interval since last treatment

          -  New York Heart Association classification III or IV, known symptomatic coronary artery
             disease, or symptoms of coronary artery disease on systems review, or known cardiac
             arrhythmias (atrial fibrillation or supraventricular tachycardia [SVT])

          -  Untreated or progressive central nervous system (CNS) metastases

               -  NOTE: Patients with a history of treated brain metastases (surgical resection,
                  whole brain radiation, and/or stereotactic radiosurgery) are eligible only if
                  they are asymptomatic and have stable MRI scans for 3 consecutive months,
                  including < 28 days of study entry

          -  Standing requirement for blood product support

          -  Human immunodeficiency virus (HIV) positive test result or history of other
             immunodeficiency

          -  History of organ transplantation

          -  History of chronic hepatitis B or C

          -  Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy
             considered investigational (utilized for a non-Food and Drug Administration
             [FDA]-approved indication and in the context of a research investigation)

          -  Any concurrent medications that the principal investigator determines could interfere
             with the trial

          -  Treatment with oral/systemic corticosteroids, with the exception of topical or inhaled
             steroids

          -  Exposure to household contacts =< 15 months old or household contact with known
             immunodeficiency

          -  Allergy to measles vaccine or history of severe reaction to prior measles vaccination

          -  History of receiving the measles vaccination with the "killed vaccine" between
             1963-1967 without subsequent re-immunization (2 doses) with the active, live
             vaccination."