Inclusion Criteria:

- Serum creatinine =< 2.5 mg/dL

- Absolute neutrophil count >= 1000/uL

- Untransfused platelet count >= 75000/uL

- Hemoglobin >= 8 g/dL

- Total bilirubin =< 1.5 times institutional upper limit of normal (ULN)

- Patients with relapsed multiple myeloma who have already received one or more
standard treatment regimens

- Measurable disease of multiple myeloma as defined by at least ONE of the following:

- Serum monoclonal protein >= 1 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

- Monoclonal bone marrow plasmacytosis >= 30% (evaluable disease) (myeloma
protocols only)

- Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2

- Adequate residual organ function per treating physician discretion; Note: there is no
limit with regard to the number of prior therapies

- Provide informed written consent

- Negative pregnancy test done =< 7 days prior to registration, for women of
childbearing potential only

- Willing to provide samples for correlative research purposes

- Willing to return to consenting institution for follow-up during the study

- Recovered (i.e., =< grade 1 toxicity) from the reversible effects of prior
antineoplastic therapy

Exclusion Criteria:

- Any of the following recent therapies:

- Alkylators (e.g. melphalan, cyclophosphamide) =< 14 days prior to registration

- Anthracyclines =< 14 days prior to registration

- High dose corticosteroids, immune modulatory drugs (thalidomide or
lenalidomide), or proteosome inhibitors (bortezomib) =< 7 days prior to
registration

- Concomitant high dose corticosteroids (concurrent use of corticosteroids); EXCEPTION:
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.

- Other active malignancy =< 2 years prior to registration; EXCEPTIONS: non-melanotic
skin cancer or carcinoma in-situ of the cervix; NOTE: if there is a history of prior
malignancy, they must not be receiving other specific treatment for their cancer

- Any of the following:

- Pregnant women or women of reproductive ability who are unwilling to use 2
effective methods of contraception from the time of signing the informed consent
form through 30 days after the last dose of study drug

- Nursing women

- Men who are unwilling to use a condom (even if they have undergone a prior
vasectomy) while having intercourse with any woman, while taking the drug and
for 30 days after stopping treatment

- Other co-morbidity which would interfere with patient's ability to participate in
trial, e.g. uncontrolled infection, uncompensated heart or lung disease

- Other concurrent chemotherapy, radiotherapy, or any ancillary therapy considered
investigational; NOTE: bisphosphonates are considered to be supportive care rather
than therapy, and are thus allowed while on protocol treatment

- Peripheral neuropathy >= grade 2 on clinical examination during the screening period

- Major surgery =< 14 days prior to registration

- Currently taking strong or moderate inhibitors/inducers of cytochrome P450 3A4
(CYP3A4); Note: dinaciclib is a CYP3A4 substrate; patients should not take
grapefruit/grapefruit juice or St. John's Wort; use of strong or moderate CYP3A4
inhibitors or CYP3A4 inducers is prohibited from =< 7 days prior to registration

- Any of the following conditions:

- Myocardial infarction =< 6 months prior to registration or has New York Heart
Association (NYHA) class III or IV heart failure

- Uncontrolled angina

- Severe uncontrolled ventricular arrhythmias

- Electrocardiographic evidence of acute ischemia

- Active conduction system abnormalities; NOTE: prior to study entry, any
electrocardiogram (ECG) abnormality at screening must be documented by the
investigator as not medically relevant

- Known hypersensitivity to bortezomib, boron, or mannitol

- Serious medical or psychiatric illness likely to interfere with participation in this
clinical study per the judgment of the treating physician