Pilot Study Estradiol Followed by Exemestane Hormone Receptor + Metastatic Breast Cancer

Inclusion Criteria: * Post-menopausal women with metastatic carcinoma of the breast; post-menopausal, as defined by at least one of the following: at least 12 months without spontaneous menstrual bleeding, history of bilateral salpingo-oophorectomy with or without hysterectomy, age \> 55 with hysterectomy with or without oophorectomy, serum Follicle-stimulating hormone (FSH) in post-menopausal range within 4 weeks of registration. * Positive for estrogen receptor (ER) or progesterone receptor (PgR) with positivity defined as immunohistochemical staining in \>= 10% of cells * Either measurable disease by RECIST or non-measurable evaluable disease; tests to evaluate disease (measurable and non-measurable) must be completed within 28 days prior to registration; these will include a CT scan of the chest/abdomen/pelvis and a bone scan; patients with effusions or ascites as the only sites of disease are ineligible * Performance status of 0-2 by Zubrod criteria * Patients must have a baseline CA15-3 or CA 27.29 measurement for future comparison, but any baseline value is acceptable * Patients must have had prior aromatase inhibitor (AI) therapy in the metastatic setting (any number of prior AI is allowed, this may have been any of the AI's), or have developed metastatic disease on adjuvant AI therapy; prior treatment with tamoxifen and/or fulvestrant is also allowed; patients must not have been previously treated with estradiol for metastatic breast cancer * Patients must be able to take oral medications * Patients must be informed of the investigational nature of this study and give written informed consent in accordance with institutional and federal guidelines * Patients must consent to the serum and CTC blood specimen submissions Exclusion Criteria: * Planning to receive concomitant chemotherapy, hormone therapy (including hormone replacement therapy), radiation therapy, or antibody therapy for malignancy while receiving protocol treatment, with the single exception of trastuzumab; concomitant trastuzumab will be allowed for Her-2 positive patients who were previously on trastuzumab; patients who have had previous radiotherapy must complete treatment within 4 weeks of registration, and have recovered from acute toxicity from radiation; patients with prior cytotoxic chemotherapy for metastatic disease will not be eligible * Known hypersensitivity or intolerance to estradiol, aromatase inhibitors, or aspirin; patients must not have a history of aspirin-induced GI bleeding within the past 3 years * Known untreated brain or CNS metastases due to the risk of bleeding on aspirin during estradiol * History of deep vein thrombosis, pulmonary embolism, or other clot requiring anticoagulation; patients must not have a known inherited hypercoagulable disorder * History of decompensated congestive heart failure, unstable angina, or uncontrolled psychiatric illness which would limit compliance with the protocol treatment * Prior malignancy except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated Stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease-free for 5 years