Patient description: The patient is a 45-year-old postmenopausal woman with cytologically confirmed breast cancer. A core biopsy revealed a 3 cm invasive ductal breast carcinoma in the left upper outer quadrant. The tumor is HER2-positive and ER/PR negative. Axillary sampling revealed 5 positive lymph nodes. CXR was remarkable for metastatic lesions. The patient is using multivitamins and iron supplements. She does not smoke or consume alcohol. She is not sexually active and has no children. She is a candidate for tumor resection and agrees to do so prior to chemotherapy.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Human Epidermal Growth Factor 2 Negative Carcinoma of Breast Hormone Receptor (HR)-Positive Breast Cancer Participants must meet the following on screening examination to be eligible to participate in the study. Laboratory tests required for must be completed within 14 days prior to the date of registration. Diagnostic tests, such as MRIs and CT scans, must be performed within 30 days of registration and baseline measurements must be documented within 14 days of the date of registration Participants with histologically or cytologically confirmed hormone receptor (HR)-positive, Her2-negative metastatic breast cancer. Central confirmation of HR positivity is not required Postmenopausal women as defined as Age >60 years -- Age >45 with intact uterus and amenorrhea for ≥ 12 consecutive months or Follicle stimulating hormone (FSH) levels within postmenopausal range according to the ranges established by the testing facility -- Premenopausal women who have been on a GnRH agonist for at least 6 weeks prior to study entry. Women in this group MUST remain on the GnRH agonist for the duration of protocol treatment -- Status post bilateral oophorectomy, after adequate healing post surgery Men are eligible, as long as on a GnRH agonist for at least 6 weeks prior to study entry. Men MUST remain on the GnRH agonist for the duration of protocol treatment Participants must have measurable disease as per 1.1 Prior Treatment Specifics  Participants who have demonstrated intolerance to 125mg of Palbociclib are ineligible for the Phase I portion Participants who are receiving any other investigational agents Participants who have received previous treatment with an mTOR inhibitor or exemestane Participants with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to palbociclib, everolimus or exemestane Participants with known brain metastases may be enrolled in this study if radiation therapy and/or surgery have been completed with a minimum of 3 months of stable disease demonstrated on serial evaluation by CT (with contrast enhancement) or MRI. Such participants must no longer require treatment with corticosteroids or enzyme inducing anti-epileptic medications for their CNS disease Participants with bilateral diffuse lymphangitic carcinomatosis Participants with significant symptomatic deterioration of lung function. If clinically indicated, pulmonary function tests including measures of predicted lung volumes, DLco, O2 saturation at rest on room air should be considered to restrictive pulmonary disease, pneumonitis or pulmonary infiltrates Evidence of current pneumonitis Subjects with organ allograft requiring immunosuppression Participants with uncontrolled intercurrent illness including, but not limited to