INCLUSION CRITERIA for all subjects:  Written informed consent and HIPAA authorization for release of personal health information signed by the subject or his/her legally authorized representative. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. Age greater than or equal to 18 years at the time of consent. Because no dosing or adverse event data are currently available on the use of belantamab mafodotin as a single agent or in combination with KRd in subjects less than 18 years of age, children are excluded from this study. ECOG Performance Status of less than or equal to 2 Demonstrate adequate organ function  Adequate cardiac function as defined by a greater than 40% left ventricular ejection fraction (LVEF) by ECHO, cardiac MRI or MUGA  Note for subjects in phase II: if a cycle of pre-study induction therapy containing a PI or anthracycline was administered, assessment of the LVEF must be repeated. For those with symptomatic pulmonary disease with Grade 2 or higher symptoms (e.g. COPD, asthma) or other signs / symptoms of pulmonary disease, adequate pulmonary function as defined by a FEV1 greater than or equal to 50% of predicted and DLCO/VA greater than or equal to 50% of predicted Females of childbearing potential (FCBP) must have two negative serum pregnancy tests during screening: the first within 10-14 days prior to first dose of study treatment and the second within 24 hours prior to first dose of study treatment. NOTE: Females are considered of childbearing potential unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy), are amenorrhoeic for less than 2 years without history of a hysterectomy and oophorectomy must have a follicle stimulating hormone value in the postmenopausal range upon screening evaluation; or are postmenopausal (at least 12 consecutive months with no menses without an alternative medical cause). FCBP must be willing to use 2 effective contraceptive methods (at least one that is highly effective) or abstinence starting from the time of informed consent, while on belantamab mafodotin and lenalidomide. If either drug is discontinued, 2 effective forms of contraception should be continued until at least 4 weeks after the last dose of lenalidomide, and 1 form of effective contraception should be continued until 4 months post last dose of belantamab mafodotin. FCBP should use effective contraception or abstinence from consent until 30 days after last treatment with carfilzomib, and males with a partner of childbearing potential must use effective contraception or abstinence for at least 90 days post last dose of carfilzomib.  Male subjects must agree to the following from the first dose of study treatment until 6 months after the last dose of belantamab mafodotin, to allow for clearance of altered sperm:  Refrain from donating sperm  PLUS either:  Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent. OR Must agree to use effective contraception/barrier as detailed below:  Agree to use a male condom, even if they have undergone a successful vasectomy, and female partner of reproductive potential to use an additional highly effective contraceptive method with a failure rate of less than 1% per year 10. FCBP must agree not to donate eggs (ova, oocytes) for the purpose of reproduction during the intervention period and for at least 4 months after the last dose of study intervention belantamab mafodotin, at least 30 days after the last dose of carfilzomib, and at least 4 weeks after the last dose of lenalidomide.  11. As determined by the enrolling physician, ability of the subject to understand and adhere with study procedures for the entire length of the study 12. Ability to swallow oral medications 13. Willing to refrain from using contact lenses while participating in this study  INCLUSION CRITERIA - Phase I treatment for Relapsed or Relapsed/Refractory MM:  Subjects with Relapsed or Relapsed/Refractory MM who have had 1-3 lines of prior therapy.  a. Refractory is defined as less than 25% reduction in M-protein or progression of disease during treatment or within 60 days after cessation of treatment b. A line of therapy is defined as one or more cycles of a planned treatment program.  This may consist of one or more planned cycles of single-agent therapy or combination therapy, as well as a sequence of treatments administered in a planned manner. A new line of therapy starts when a planned course of therapy is modified to include other treatment agents (alone or in combination) as a result of disease progression, relapse, or toxicity. A new line of therapy also starts when a planned period of observation off therapy is interrupted by a need for additional treatment for the disease.  Subjects must have measurable disease, as defined by at least one of the following:  a. Serum monoclonal protein level greater than or equal to 0.5 g/dL b. 24-hour urinary M-protein greater than or equal to 200 mg c. Involved free light chain level greater than or equal to 10 mg/dL, along with an abnormal free light chain ratio.  Subject must have not progressed on full dose lenalidomide previously (25 mg on days 1-21 of a 28-day cycle or its dosing equivalent based on renal function at the time of progression)  Prior to enrollment:  a. There should be a washout period of ≥14 days from any prior chemotherapy AND b. The subject must have adequate recovery from toxicity of prior chemotherapy as defined by the following: i. Hematologic lab results within parameters noted in Table 3.2.1 ii. Non-hematologic toxicity resolved to grade 1 or baseline with the following exceptions:  Subjects who have started a course of antibiotic therapy for infection and symptoms have improved to baseline or grade 1, but remain on antibiotic therapy are eligible Subjects with ≤grade 2 fatigue are eligible Subjects with ≤grade 2 hyperglycemia are eligible, even if pharmacologic treatment was required Subjects with ≤grade 2 electrolyte abnormalities are eligible, even if pharmacologic treatment was required Subjects with ≤grade 2 nausea, constipation or diarrhea are eligible, even if pharmacologic treatment was required  INCLUSION CRITERIA - Phase II treatment for high-risk newly diagnosed MM:  1. Active, newly diagnosed multiple myeloma with CRAB features or a myeloma-defining event per the IMWG 2014 criteria. Note: It is acceptable to include subjects who have had one cycle of emergent treatment for multiple myeloma.  2. High-risk disease, as defined by at least one of the following: i. Del(1p) ii. Gain of 1q21 [greater than or equal to 3 copies] iii. Monosomy 13 or del(13q) by conventional karyotype iv. High risk IgH translocation [t(4;14), t(14;16) or t(14;20)] v. del(17p) 3. Measurable disease by 1 or more of the following:  Serum monoclonal protein level greater than or equal to 0.5 g/dL 24-hour urinary M-protein greater than or equal to 200 mg Involved free light chain level greater than or equal to 10 mg/dL (100 mg/L), along with an abnormal free light chain ratio. Note: for subjects who have received a prior cycle of non-protocol therapy, measurable disease will be based on the serum and urine monoclonal protein and serum free light chain levels prior to the cycle of non-protocol therapy 4. No more than one prior cycle of non-protocol therapy will be allowed, recognizing that high-risk multiple myeloma subjects frequently require immediate therapy at initial diagnosis even before risk assessment is complete. For those subjects who receive a cycle of non-protocol induction therapy:  a. There should be a washout period of ≥14 days from the last dose of pre-study therapy AND b. The subject must have adequate recovery from toxicity of pre-study therapy as defined by the following: i. Hematologic lab results within parameters ii. Non-hematologic toxicity resolved to grade 1 or baseline with the following exceptions:  Subjects who have started a course of antibiotic therapy for infection and symptoms have improved to baseline or grade 1, but remain on antibiotic therapy are eligible Subjects with less than or equal to grade 2 fatigue are eligible Subjects with less than or equal to grade 2 hyperglycemia are eligible, even if pharmacologic treatment was required Subjects with less than or equal to grade 2 electrolyte abnormalities are eligible, even if pharmacologic treatment was required Subjects with less than or equal to grade 2 nausea, constipation or diarrhea are eligible, even if pharmacologic treatment was required  EXCLUSION CRITERIA for all subjects:  Active infection requiring systemic therapy. NOTE: at the discretion of the treating investigator, subjects who have started antibiotic therapy for subjects who had symptoms present, symptoms must have improved to baseline or grade 1 in severity may start treatment prior to completion of their course of antibiotic therapy. Pregnant or breastfeeding (NOTE: breast milk cannot be stored for future use while the mother is being treated on study.)  Subjects cannot have other prior or concomitant malignancies except for:  Curatively treated non-melanoma skin cancer Other cancer for which the subject has been medically stable for at least 2 years and/or, in the opinion of the Site Principal Investigators, will not affect the evaluation of the effects of clinical trial treatments on the currently targeted malignancy Active central nervous system (CNS) involvement Concomitant AL amyloidosis or POEMS syndrome Plasma cell leukemia Treatment with any investigational drug within 14 days or five half-lives, whichever is shorter, prior to first dose of study treatment. Medical, psychiatric, or other condition/disorder (including lab abnormalities) which, in the opinion of the treating physician, would make this protocol treatment unreasonably hazardous for the subject, or could interfere with obtaining informed consent or compliance to the study procedures  Significant cardiac disease, including any of the following:  Greater than or equal to Class 3 New York Heart Association (NYHA) congestive heart failure (see Appendix B) ECG evidence of acute ischemia Unstable angina Myocardial infarction, Coronary angioplasty, stenting, or bypass grafting within three months prior to day 1 of treatment Clinically significant uncontrolled and/or untreated arrhythmias or conduction block, including clinically significant ECG abnormalities such as 2nd degree Mobitz Type ll or 3rd degree atrioventricular (AV)block. However, PACs, PVCs, rate controlled atrial fibrillation, sinus arrhythmia, asymptomatic sinus bradycardia or sinus tachycardia and 1st degree heart block are not considered clinically significant. Greater than or equal to Grade 2 QTcF prolongation (i.e. >480 msec) Uncontrolled hypertension, defined as a systolic blood pressure of greater than or equal to 160 mmHg or a diastolic blood pressure of greater than or equal to 90 mmHg Grade greater than or equal to 2 peripheral neuropathy Psychiatric illness/social situation that would limit compliance with study requirements as determined by the investigator Known immediate or delayed hypersensitivity or allergic reaction to any components of, or related to, protocol therapy (e.g. during exposure to carfilzomib, lenalidomide or dexamethasone as part of a pre-study cycle of therapy). History of erythema multiforme to lenalidomide or other IMID Discontinuation of prior carfilzomib, lenalidomide or dexamethasone due to treatment toxicity Major surgery within 4 weeks prior to day 1 of treatment Radiation within 14 days prior to day 1 of treatment. Note: palliative XRT to less than 5% of the total marrow volume as assessed by the treating investigator is allowed within 14 days prior to day 1 of treatment Current corneal epithelial disease except mild changes in corneal epithelium  Positive hepatitis C antibody test result (this test preferable) or positive hepatitis C RNA test result at screening or within 3 months prior to first dose of study treatment  a. NOTE: Subjects with positive Hepatitis C antibody due to prior eradicated disease can be enrolled if a confirmatory negative Hepatitis C RNA test is obtained  A known diagnosis of HIV Is seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen [HBsAg]). Subjects with resolved infection (i.e. subjects who are HBsAg negative but positive for antibodies to hepatitis B core antigen [anti-HBc] and/or antibodies to hepatitis B surface antigen [anti-HBs]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) DNA levels. Subjects who are PCR positive will be excluded. Subjects with Hepatitis B surface antibodies and previous Hepatitis B vaccination will be eligible. Has current unstable liver or biliary disease defined by the presence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, esophageal or gastric varices, persistent jaundice, or cirrhosis. Note: Stable non-cirrhotic chronic liver disease (including Gilbert's syndrome or asymptomatic gallstones) or hepatobiliary involvement of malignancy is acceptable if otherwise meets entry criteria Participant must not have presence of active renal condition (infection, requirement for dialysis or any other condition that could affect participant's safety). Participants with isolated proteinuria resulting from MM are eligible, provided they fulfill inclusion criteria Participant must not have had plasmapheresis within 7 days prior to first dose of study treatment Any evidence of active mucosal or internal bleeding Participant must not be simultaneously enrolled in any interventional clinical trial Administration of live or live-attenuated vaccines within 30 days prior to the first dose of study treatment