Inclusion Criteria for both Phase Ib and Phase II:
* Hormone receptor-positive, HER2-negative metastatic breast cancer.
* Measurable or non-measurable but evaluable disease by RECIST v1.1.
* Candidate for capecitabine treatment per physician decision. See below phase-specific eligibility criteria for further guidance.
* No more than one prior chemotherapy for metastatic disease.
* Patient must have received prior endocrine therapy with CDK4/6 inhibitor.
* If patient is on denosumab or zoledronic acid prior to enrollment, patient must have been on the regimen for at least 6 months prior to study. However, a washout of 3 weeks is required prior to C1D1.
* At least 18 years of age.
* ECOG performance status 0, 1, or 2
* Life expectancy of at least 12 weeks.
* Adequate bone marrow and organ function as defined below:
* Leukocytes ≥ 3 K/cumm
* Absolute neutrophil count (ANC) ≥ 1.5 K/cumm
* Platelets ≥ 100 K/cumm
* Total bilirubin ≤ 1.5 x IULN (or total bilirubin ≤ 3 mg/dL if patient has known Gilbert Syndrome)
* AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN
* Creatinine clearance \> 60 mL/min by Cockcroft-Gault
* Calcium within normal limits
* Women of childbearing potential and men who are heterosexually active must agree to use adequate contraception as specified in the protocol. Contraception should continue for 6 months (for women) or 3 months (for men) after the end of treatment. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately.
* Ability to understand and willingness to sign an IRB approved written informed consent document.
* Patients must have archival tissue sample available from prior metastatic biopsy. If no tissue is available, patient may still be able to enroll with PI approval.
Inclusion Criteria for both Phase Ib:
* Presence of bone metastasis is not required.
* Candidate for, or currently on stable doses of capecitabine, defined as capecitabine: 1000 mg/m\^2 BID, 14 days on and 7 days off. A stable dose of capecitabine is defined as no more than grade 1 AEs related to capecitabine on the 1000 mg/m\^2 BID, 14 days on and 7 days off dose for at least 1 cycle. Capecitabine is not counted as a prior chemotherapy regimen in these patients.
Inclusion Criteria for Phase II:
* Progressive bone metastasis per the most recent tumor imaging studies by RECIST 1.1 or clinical progression (such as worsening bone pain, elevation of tumor marker) per treating physician.
Exclusion Criteria for both Phase Ib and Phase II:
* Patients may not have received the following investigational or SOC therapies within the below specified time frames prior to C1D1:
* Radiation therapy within 1 week
* Systemic chemotherapy, including antibody drug conjugates with chemotherapy payload, within 3 weeks.
* Immunotherapy within 3 weeks
* Oral chemotherapy or molecularly targeted therapy within 5 half-lives of the agent.
* Endocrine therapies do not have a required washout and may be continued until C1D1.
* Strong and moderate CYP3A4 and CYP2C8 inhibitors (including grapefruit), strong and moderate CYP3A and CYP2C8 inducers, and drugs with QT prolonging potential within 5 half-lives of the agent.
* Untreated brain metastases. Patients with treated brain metastases are eligible if they show no evidence of progression and are off steroids.
* A history of allergic reactions attributed to compounds of similar chemical or biologic composition to zunsemetinib or other agents used in the study.
* History of acute, untreated skeletal related events (SRE) or active untreated SRE or a change or an anticipated change in the SOC anti-resorptive agents after entering the study.
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia.
* Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 14 days of C1D1.
* Patients with HIV are eligible unless their CD4+ T-cell counts are \< 350 cells/mcL or they have a history of AIDS-defining opportunistic infection within the 12 months prior to Cycle 1 Day 1. Concurrent treatment with effective ART according to DHHS treatment guidelines is recommended.
* Screening resting QTcF above 470 msec.
Exclusion Criteria for Phase Ib:
* Capecitabine within 2 weeks prior to C1D1. Patients may be currently taking capecitabine, but must not have dosed within 2 weeks prior to C1D1 for study correlative purposes.
Exclusion Criteria for Phase II:
* Prior capecitabine in the metastatic setting.
* History of other malignancy, unless all treatment was completed and patient had no evidence of disease within 2 years of C1D1.
