Pembrolizumab and Paclitaxel in Hormone Receptor-positive, hyperMUTATted Metastatic Breast Cancer Identified by Whole exOme sequeNcing ('MUTATION2')

Inclusion Criteria: 1. Male participants or female participants who are pre or postmenopausal women and at least 19 years of age on the day of signing informed consent with histologically or cytologically confirmed diagnosis of stage IV hormone receptor-positive breast cancer will be enrolled in this study. 2. A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: 1. Not a woman of childbearing potential (WOCBP) as defined in Appendix 3 OR 2. a WOCBP must agree to use a contraception as detailed in Appendix 3 of this protocol during the treatment period and for at least 120 days, corresponding to time needed to eliminate any study treatments \[e.g., 5 terminal half-lives for pembrolizumab and paclitaxel (52.7 hours)\] after the last dose of study treatment. 3. No prior systemic cytotoxic chemotherapy in the metastatic setting. Lines of endocrine or HER2-targeted therapy are not limited. \* No prior paclitaxel, except ≥12 months after last dose of chemotherapy for early breast cancer (if chemotherapy given) 4. Criteria of hypermutation should be met. \*Criteria of hypermutation: 70 nonsynonymous mutations per tumor per exome as the presumptive starting cut-off for upper 20% of mutation burden. we will revise cut-off after enrolling every 30 patients. That is, the criteria of hypermutation will be altered every 30 cases. 5. The participant (or legally acceptable representative if applicable) provides written informed consent for the trial. 6. Have measurable disease based on RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. 7. Subject who has biopsy-accessible tumor for WES. Biopsy on breast tumor or axillary nodes is acceptable if locoregional recurrence after primary surgery occurs or de novo stage IV breast cancer is diagnosed 8. Documented disease progression on the most recent therapy. This is not applicable during prescreening phase. That is, tissue biopsy is possible while maintaining existing treatment. 9. Life expectancy of \> 12 weeks 10. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 Evaluation of ECOG is to be performed within 7 days prior to the date of allocation/randomization. 11. Have adequate organ function as defined in the following table(Table 2). Specimens must be collected within 10 days prior to the start of study treatment. Exclusion Criteria: 1. A WOCBP who has a positive urine pregnancy test within 72 hours prior to allocation. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 2. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX 40, CD137). 3. Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks \[could consider shorter interval for kinase inhibitors or other short half-life drugs\] prior to allocation. 4. Has received prior radiotherapy within 2 weeks of start of study intervention. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease. 5. Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed. 6. Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study intervention. * Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. 7. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. 8. Has a history of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years. * Note: The time requirement does not apply to participants who underwent successful definitive resection of basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, in situ cervical cancer, or other in-situ cancers 9. Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases (eg., whole brain radiation therapy, gamma-knife surgery or brain tumor removal) may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study intervention. 10. Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients. 11. Has hypersensitivity (≥Grade 2 peripheral neuropathy) or contraindication to paclitaxel or any of its excipients. 12. Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. 13. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 14. Has an active infection requiring systemic therapy. 15. Has a known history of Human Immunodeficiency Virus (HIV) infection: HIV-1 or HIV-2 antibody+ or HTLV-1 antibody+ 16. Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. 1. Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as having a negative HBsAg test and a positive hepatitis B core antibody \[HBcAb\] test, accompanied by a negative HBV DNA test) are eligible. 2. Patients positive for HCV antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA. 17. Has a known history of active TB (Bacillus Tuberculosis). 18. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 19. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 20. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment. 21. Has had an allogenic tissue/solid organ transplant.