Mirvetuximab Soravtansine as First Line in Treating Patients With Triple Negative Breast Cancer

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Confirmed invasive triple-negative breast cancer defined as estrogen receptor (ER) \< 10%; progesterone receptor (PR) \< 10% by immunohistochemistry (IHC) and HER2 0-1+ by IHC or 2+, fluorescence in situ hybridization (FISH) \< 2, gene copy number \< 4 * (For Cohort A) - Archived tissue available at pre-screening to confirm FR alpha+ breast cancer * (For Cohort A) Archived tissue available pre-screening to confirm FR alpha+ breast cancer. (For Cohort B) Confirmed FRalpha+ breast cancer defined as low FRalpha expression: \>= 25% of cells having \>= 1+ expression * (For Cohort A) Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST). (For cohort B) Clinical or radiologic primary tumor size of at least 1.5 cm prior to enrollment onto protocol 2014-0185 (ARTEMIS). Primary tumor of at least 1.0 cm or evidence of continued lymph node involvement by imaging (ultrasound or magnetic resonance imaging \[MRI\]) after adriamycin-based neoadjuvant therapy * (For cohort B): Primary tumor sample collected before NACT started (on ARTEMIS) and underwent molecular testing for integral biomarkers including immunohistochemical assessment of FRalpha * (For cohort A): No limit on prior therapies for metastatic disease. (Relapse of disease within 6 months of adjuvant or neoadjuvant chemotherapy is considered 1 line of therapy for metastatic disease). (For cohort B): received at least one dose of an anthracycline-based NACT. Patients are eligible if therapy was discontinued due to disease progression or therapy intolerance. Patients with disease progression on anthracycline-based therapy should be evaluated by the surgical team. If the patient is deemed inoperable at the time of evaluation, the patient may continue to undergo protocol therapy with a goal of reduction in tumor size to become operable. If the patient is deemed at high risk of becoming inoperable by the surgical team based upon tumor size or location, the patient will be considered ineligible for study and will be recommended to go to surgery * (For cohort B): Primary tumor size of at least 1.0 cm by imaging (ultrasound or MRI) or evidence of continued lymph node involvement by imaging (ultrasound or MRI) after adriamycin-based neoadjuvant therapy * (For cohort B): Baseline multigated acquisition (MUGA) or echocardiogram showing left ventricular ejection fraction (LVEF) \>= 50% within 6 weeks prior to initiation of NACT * (For both cohorts A and B): Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * (For both cohorts A and B): Platelets \>= 100 x 10\^9/L * (For both cohorts A and B): Hemoglobin (Hb) \> 9 G/dL * (For both cohorts A and B): Total serum bilirubin =\< 2.0 mg/dL * (For both cohorts A and B): Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x upper limit of normal (ULN) (=\< 5 x ULN in patients with liver metastases) * (For both cohorts A and B): International normalized ratio (INR) =\< 2 * (For both cohorts A and B): Serum creatinine =\< 1.5 x ULN * (For both cohorts A and B): Serum albumin \> 2 * Signed informed consent obtained prior to any screening procedures * (For cohort A only): Time from prior therapy: a. Systemic anti-neoplastic therapy: five half-lives or four weeks, whichever is shorter. Hormonal therapy is not considered anti-neoplastic therapy. b. Radiotherapy: wide-field radiotherapy (e.g. \> 30% of marrow-bearing bones) completed at least four weeks, or focal radiation completed at least two weeks, prior to starting study treatment * (For cohort B only): Patients must have at least 3 and no more than 5 weeks between anthracycline-based therapy and start of treatment with mirvetuximab soravtansine * (For both cohorts A and B): Patients must have resolution of toxic effect(s) of the most recent prior chemotherapy to grade 1 or less (except alopecia) * (For both cohorts A and B): Women of child-hearing potential (WCBP) must have a negative pregnancy test within 3 days prior to the first dose of study treatment Exclusion Criteria: * Pregnant or lactating women * Patients with a history of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study * (For Cohort B only): Presence of metastatic disease or prior radiation therapy of the primary breast carcinoma or axillary lymph nodes * Women of child-bearing potential (WCBP), defined as all women capable of becoming pregnant, won't use highly effective methods of contraception during the study and 12 weeks after. Highly effective contraception methods include combination of any two of the following: * Placement of an intrauterine device (IUD) or intrauterine system (IUS) * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository * Total abstinence or * Male/female sterilization * Women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile, or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks prior to study entry. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of childbearing potential * Male patients whose sexual partner(s) are WCBP who are not willing to use adequate contraception, during the study and for 12 weeks after the end of treatment * Patients with \> grade 1 peripheral neuropathy * Active or chronic corneal disorder, including but not limited to the following: Sjogren's syndrome, Fuchs corneal dystrophy (requiring treatment), history of corneal transplantation, active herpetic keratitis, and also active ocular conditions requiring on-going treatment/monitoring such as wet age-related macular degeneration requiring intravitreal injections, active diabetic retinopathy with macular edema, presence of papilledema, and acquired monocular vision * Serious concurrent illness or clinically-relevant active infection, including, but not limited to the following: * Known active hepatitis B or C * Known human immunodeficiency virus (HIV) infection * Varicella-zoster virus (shingles) * Cytomegalovirus infection * Any other known concurrent infectious disease, requiring IV antibiotics within 2 weeks of study enrollment * Clinically-significant cardiac disease: * Recent myocardial infarction (=\< 6 months prior to day 1) * Unstable angina pectoris * Uncontrolled congestive heart failure (New York Heart Association \> class II) * Uncontrolled hypertension (\>= Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\]4.03 grade 3) * Prior history of hypertensive crisis or hypertensive encephalopathy * Uncontrolled cardiac arrhythmias * Clinically-significant vascular disease (e.g. aortic aneurysm, or dissecting aneurysm) * Severe aortic stenosis * Clinically significant peripheral vascular disease * \>= Grade 3 cardiac toxicity following prior chemotherapy * Corrected QT interval (QTc) \> 470 for females and \> 450 for males * History of neurological conditions that would confound assessment of treatment-emergent neuropathy * History of hemorrhagic or ischemic stroke within the last 6 months * History of cirrhotic liver disease * Previous clinical diagnosis of non-infectious pneumonitis or non-infectious interstitial lung disease * Prior hypersensitivity to monoclonal antibodies * Patients who have a history of another primary malignancy, with the exceptions of: non-melanoma skin cancer, and carcinoma in situ of the cervix, uteri, or breast from which the patient has been disease free for \>= 3 years * Carcinomatous meningitis, untreated central nervous system (CNS) disease or symptomatic CNS metastasis. Patients with previously treated CNS metastasis (excluding carcinomatous meningitis) may participate if they are stable (without evidence of progression by imaging, using identical imaging modality at each assessment, for at least 4 weeks prior to first dose of study treatment), have no evidence of new or emerging CNS metastasis, and are not using steroids for at least 7 days prior to first dose of study treatment * History or evidence of thrombotic or hemorrhagic disorders within 6 months before first study treatment * Required used of folate-containing supplements (e.g. folate deficiency)