Inclusion Criteria:  Patients must have a histologically or cytologically confirmed diagnosis of breast cancer with a clinical diagnosis of IBC  IBC diagnosis is based on the current or previous clinical evaluation demonstrating inflammatory changes in the involved breast. Pathological evidence of dermal lymphatic invasion should be noted but is not required for diagnosis. Diagnosis of IBC defined by:  Rapid onset of breast erythema, edema and/or peau d'orange, and/or warm breast, with or without an underlying palpable mass Duration of history no more than six months Erythema occupying at least one-third of the breast Triple negative metastatic tumor, negative for hormone receptor and negative for HER2 as defined by the 2018 American Society of Clinical Oncology (ASCO)/ College of American Pathologists (CAP) guidelines Patients must have stage IV M1 measurable or evaluable disease as defined by RECIST v1.1, or non-measurable tumors Patient's tumors must express PD-L1 with a Combined Positive Score of >= 10 as determined by the PD-L1 Immunohistochemistry (IHC) 22C3 pharmDx assay  Patients must have progressed on >= 1 prior systemic therapy for metastatic disease (prior therapies include standard neoadjuvant chemotherapy with anthracycline and taxane)  Note: A 28 day wash out period for prior therapy before beginning study treatment is required Patients must be age >= 18 years Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 at registration Leukocytes >= 2,000/mcL (within 14 days prior to registration) Absolute neutrophil count >= 1,500/mcL (within 14 days prior to registration) Platelets >= 100,000/mcl (within 14 days prior to registration)  Hemoglobin >= 9 g/dL or >= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) (within 14 days prior to registration)  Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks Total bilirubin =< 1.5 x upper limit of normal (ULN) OR direct bilirubin =< ULN for participants with total bilirubin levels > 1.5 x ULN (within 14 days prior to registration) Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum pyruvic glutamic transaminase [SPGT]) =< 2.5 X ULN (within 14 days prior to registration)  Creatinine =< 1.5 x ULN OR measured or calculated creatinine clearance (CrCl) (glomerular filtration rate [GFR] can also be used in place of creatinine or CrCl) >= 60 mL/min/1.73 m^2 (within 14 days prior to registration)  Creatinine clearance (CrCl) should be calculated per institutional standard International normalized ratio (INR) OR prothrombin time (PT) =< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or activated partial thromboplastin time (aPTT) is within therapeutic range of intended use of anticoagulants (within 14 days prior to registration)  Females of child-bearing potential (FOCBP) and males must agree to use adequate contraception prior to study entry, for the duration of study participation, and for 5 half-lives (130 days) following completion of therapy. Should a female patient become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately  NOTE: A FOCBP is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria:  Has not undergone a hysterectomy or bilateral oophorectomy Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for > 12 months)  FOCBP must have a negative pregnancy test within 72 hours prior to registration on study  Note: Urine pregnancy test will be used first and then serum test if confirmation is needed Note: In the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication Patients must have the ability to understand and the willingness to sign a written informed consent prior to registration on study  Exclusion Criteria:  Patients who have not recovered to =< grade 1 from adverse events from chemotherapy, radiotherapy, surgery, or experimental therapies prior to entering the study are not eligible. Peripheral neuropathy must have recovered to =< grade 2  Note: If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment Patients concurrently receiving any other investigational agents are not eligible Patients who have received prior radiotherapy within 14 days of registration are not eligible. 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-central nervous system (CNS) disease  Patients who are currently participating in or have participated in a study of an investigational agent or have used an investigational device within 5 half-lives or 14 days (whichever is shorter) prior to the first dose of study treatment are not eligible  Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been >= 14 days after the last dose of the previous investigational agent Patients who have a history of allergic reactions or severe hypersensitivity attributed to compounds of similar chemical or biologic composition to pembrolizumab, carboplatin, or SGT-53 are not eligible Patients who have had prior exposure to compounds of similar chemical or biologic composition to pembrolizumab (antibodies to PD-1, PD-L1, PD-L2) or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX-40, CD137) in the metastatic setting are not eligible. Please contact the principle investigator for specific questions or interactions  Patients with active autoimmune disease or history (within 2 years) of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including chronic prolonged systemic corticosteroids (defined as corticosteroid use of duration one month or greater), are not eligible. These include but are not limited to patients with a history of:  Immune related neurologic disease Multiple sclerosis Autoimmune (demyelinating) neuropathy Guillain-Barre syndrome Myasthenia gravis Systemic autoimmune disease such as systemic lupus erythematosus (SLE) Connective tissue diseases Scleroderma Inflammatory bowel disease (IBD) Crohn's Ulcerative colitis Patients with a history of toxic epidermal necrolysis (TEN) Stevens-Johnson syndrome Anti-phospholipid syndrome NOTE: Subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll  Any condition requiring systemic treatment with corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 7 days prior to first dose of study drug  NOTE: Inhaled steroids and adrenal replacement steroid doses > 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. A brief (less than 3 weeks) course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by a contact allergen) is permitted  Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following, are not eligible:  Hypertension that is not controlled on medication Ongoing or active infection requiring systemic treatment Symptomatic congestive heart failure Unstable angina pectoris Cardiac arrhythmia Psychiatric illness/social situations that would limit compliance with study requirements Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints  A FOCBP who has a positive urine pregnancy test within 72 hours prior to registration is not eligible. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required  NOTE: in the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication Female patients who are nursing are not eligible  Patients who have a known additional malignancy that is progressing or has required active treatment within the past 2 years  NOTE: The following prior malignancies are allowed on study: 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 at least three years Patients who have a known active CNS metastases and/or carcinomatous meningitis are not eligible. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 28 days 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 treatment  Patients with a known history of hepatitis B (defined as hepatitis B surface antigen [HBsAg] reactive) or known active hepatitis C virus (defined as HCV ribonucleic acid [RNA] [qualitative] is detected) infection  NOTE: No testing for hepatitis B and hepatitis C is required unless mandated by local health authority Patients with a known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) are not eligible Patients with a known history of active TB (Bacillus tuberculosis) are not eligible Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis 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 Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 130 days after the last dose of trial treatment  Patients who have received a live attenuated vaccine =< 30 days prior to registration are not eligible  NOTE: Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed