Dinaciclib in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Relapsed or refractory multiple myeloma * Measurable disease as defined by at least ONE of the following: * Serum monoclonal protein \>= 1.0 g/dL * \> 200 mg of monoclonal protein in the urine on 24 hour electrophoresis * Serum immunoglobulin free light chain \>= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio * ≤ 5 prior therapies; stem cell transplantation and preceding induction therapy will be considered as one therapy; NOTE: Patients must not be candidates for stem cell transplantation or should have had stem cells collected previously * Life expectancy of ≥ 3 months * ECOG performance status of 0, 1 or 2 * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 75,000/mcL * Hemoglobin \>= 8 g/dL * Total serum bilirubin within normal institutional limits * AST (SGOT)/ALT(SGPT) =\< 2.5 X institutional ULN * Creatinine \< 2.5 mg/dL * Negative serum pregnancy test done ≤7 days prior to registration (for women of childbearing potential only); NOTE: Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Willingness to provide blood and bone marrow samples for mandatory research component of this study; (US sites only) Exclusion Criteria: * Any of the following prior therapies: * Myelosuppressive therapy for myeloma ≤ 3 weeks prior to registration or those who have not recovered from acute reversible adverse events due to agents administered \> 3 weeks earlier * Non-myelosuppressive agents like thalidomide or high dose corticosteroids ≤ 2 weeks prior to registration * Receiving any other investigational agents * Concomitant high dose corticosteroids * NOTE: Concurrent use of corticosteroids, but patients may be on chronic steroids (maximum dose 20 mg/day prednisone equivalent) if they are being given for disorders other than amyloid, i.e., adrenal insufficiency, rheumatoid arthritis, etc. * NOTE: Bisphosphonates are considered to be supportive care rather than therapy, and are thus allowed while on protocol treatment * Active malignancy with the exception of non melanoma skin cancer or in situ cervical or breast cancer * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infections or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or nursing women; NOTE: Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with SCH 727965, breastfeeding should be discontinued if the mother is treated with SCH 727965 * Currently taking inhibitors/inducers of CYP3A4; (SCH 727965 metabolizes via the CYP3A4 enzyme; there are potential drug interactions with concomitant use of CYP3A4 potent inhibitors/inducers; Principal Investigator should review each case and determine if patients on the CYP3A4 potent inhibitors/inducers are eligible and will make all effort to switch to alternative drugs; patients should not take grapefruit/ grapefruit juice or St. Johns' Wort) * Men or women of childbearing potential who are unwilling to employ adequate contraception