• Subjects must have histologically confirmed diagnosis of multiple myeloma

• Subjects must have measurable disease, as defined by at least one of the following:

‣ Serum monoclonal protein M-protein level \>= 0.5 g/dL

⁃ Urinary M-protein excretion of \>= 200 mg over a 24-hour period

⁃ Involved free light chain level \>= 10 mg/dL, along with an abnormal free light chain ratio

• Subjects must have disease that has relapsed and/or refractory after their most recent therapy, with progressive disease (PD) being defined as an increase of 25% from the lowest response value in any one or more of the following:

‣ Serum M-component protein (the absolute increase must be \>= 0.5 g/dL) and/or

⁃ Urine M-component protein (the absolute increase must be \>= 200 mg/24 hours) and/or

⁃ Only in subjects without a measurable serum and urine M protein level: the difference between involved and uninvolved free light chain (FLC) levels (absolute increase) must be \> 10 mg/dL

⁃ Definite development of new bone lesions or soft tissue plasmacytomas or definite increase in the size of existing bone lesions or soft tissue plasmacytomas

⁃ Development of hypercalcemia (corrected serum calcium \> 11.5 mg/dL) that can be attributed solely to the plasma cell proliferative disorder

• Subjects with one to three lines of therapy for their disease with a line of therapy defined as one or more cycles of a planned treatment program; using this definition, treatment with induction therapy, followed by high dose chemotherapy and autologous stem cell transplantation, and finally by maintenance therapy, would constitute one line, provided that multiple myeloma did not meet criteria for progression at any time during this period

• Subjects must have completed their most recent drug therapy directed at multiple myeloma in the following timeframes:

‣ Antitumor therapy (chemotherapy, antibody therapy, molecular targeted therapy, retinoid therapy, hormonal therapy, or investigational agent) at least 21 days prior to cycle 1 day 1 (C1D1) KRT-232 (AMG 232) + KRd

⁃ Corticosteroids at least 3 weeks prior to starting KRT-232 (AMG 232) + KRd, except for a dose equivalent to dexamethasone of =\< 4 mg/day

⁃ Autologous stem cell transplantation at least 12 weeks prior to starting KRT-232 (AMG 232) + KRd

⁃ Allogeneic stem cell transplantation at least 24 weeks prior to starting KRT-232 (AMG 232) + KRd, and these subjects must also NOT have moderate to severe active acute or chronic graft versus host disease (GVHD)

• Subjects must be \>= 18 years old. Because no dosing or adverse event data are currently available on the use of KRT-232 (AMG 232) in combination with KRd, subjects \< 18 years of age are excluded from this study

• Subjects must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)

• Absolute neutrophil count (ANC) \>= 1,000/mcL without growth factors within 2 week of initiation of treatment

• Platelets \>= 50,000 cells/mm\^3 if marrow plasmacytosis \< 50% OR platelet count \>= 30,000 cells/mm\^3 if marrow plasmacytosis \>= 50%

• Hemoglobin \>= 8 g/dL within 2 weeks of the initiation of treatment

• Total bilirubin \< 1.5 x institutional upper limit of normal (ULN) (\< 2.0 x ULN for subjects with documented Gilbert's syndrome or \< 3.0 x ULN for subjects for whom the indirect bilirubin level suggests an extrahepatic source of elevation)

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN

• Alkaline phosphatase \< 2.0 x ULN (if liver or bone disease are present, \< 3.0 x ULN)

• Creatinine clearance (estimated glomerular filtration rate \[eGFR\]) \>= 50 mL/min/1.73 m\^2

• Prothrombin time (PT) or partial thromboplastin time (PTT) \< 1.5 x upper limit of normal (ULN), OR international normalized ratio (INR) \< 1.5

• Subjects who have received radiation therapy targeting \> 10% of the bone marrow space must have completed this at least 2 weeks prior to starting therapy with KRT-232 (AMG 232) + KRd

• Subjects must be able and willing to provide bone marrow biopsies/aspirates and buccal swab as requested by the protocol

• Subjects must be willing to undergo myeloma genotyping for TP53 mutation, insertion, or deletion at screening

• Subjects must have an estimated life expectancy of at least 3 months

• The effects of KRT-232 (AMG 232) on the developing human fetus are unknown; for this reason and because lenalidomide is known to be teratogenic, women of child-bearing potential must commit to either abstaining continuously from heterosexual sexual intercourse or agree to use 2 forms of adequate contraception or continuously abstain from the time of informed consent for the duration of study participation through 5 weeks (women) after receiving the last dose of KRT-232 (AMG 232), lenalidomide, or carfilzomib; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 3 months after completion of KRT-232 (AMG 232) administration; this includes one highly effective form of contraception (e.g. intrauterine device \[IUD\], hormonal \[birth control pills, injections, hormonal patches, vaginal rings or implants\] or partner's vasectomy) and one additional effective contraceptive method (e.g. male latex or synthetic condom, diaphragm, or cervical cap)

• Subjects must be able to swallow medication

• Ability to understand and the willingness to sign a written informed consent document