Mirvetuximab Soravtansine and Gemcitabine Hydrochloride in Treating Patients With FRalpha-Positive Recurrent Ovarian, Primary Peritoneal, Fallopian Tube, Endometrial, or Triple Negative Breast Cancer

Inclusion Criteria: * All patients must have one of the following pathologically documented recurrent tumor types with FRalpha positivity by the Ventana immunohistochemistry (IHC): * Ovarian, primary peritoneal, fallopian tube (with exclusion of low grade, clear cell or sarcomatoid histologies for ovarian cancer) \>= 50% of tumor staining \>= 2+ intensity * Endometrial \>= 50% of tumor staining \>= 2+ intensity * TNBC confirmed by medical history of HER2-negative (confirmed by IHC 0, 1+ regardless of fluorescence in situ hybridization \[FISH\] ratio; IHC 2+ with FISH ratio \< 2.0 or HER2 gene copy \< 6.0; FISH ratio of 0, indicating gene deletion; when positive and negative in situ hybridization controls are present); estrogen receptor (ER) negative (confirmed as ER expression =\< 1% positive tumor nuclei); progesterone receptor (PR) negative (confirmed as PR expression =\< 1% positive tumor nuclei): \>= 25% of tumor staining \>= 1+ intensity * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions \>= 10 mm and short axis for nodal lesions \>= 15 mm); patients with recurrent ovarian, primary peritoneal, fallopian tube cancer may have biochemical relapse only, with baseline values of CA-125 at least 2 X upper limit of normal (ULN) * Treatment with targeted agents, immunotherapy, or hormones is allowed; patients are only eligible if they have …