Green Tea Extract in Treating Patients With Monoclonal Gammopathy of Undetermined Significance and/or Smoldering Multiple Myeloma

Inclusion Criteria: * Measurable monoclonal protein in the serum (for immunoglobin \[Ig\]G or IgM, \>= 1.0 g/dL using serum protein electrophoresis \[SPEP\]/immunofixation electrophoresis \[IFE\]; for IgA, an SPEP/IFE confirming the presence of a monoclonal IgA band plus a quantitative IgA level of \>= 750 mg/dL) OR measurable urine Bence Jones paraprotein (\>= 500mg/24hrs) OR a measurable serum free light chain (FLC), defined as an involved FLC level of \>10 mg/dl, and a serum FLC ratio that is abnormal * Neutrophil count \>= 1,500 * Platelet count \>= 100,000 * Hemoglobin \>= 9mg/dL * Alanine aminotransferase (ALT) =\< institutional upper limit of normal (IULN) * Aspartate aminotransferase (AST) =\< IULN * Total bilirubin =\< IULN * Alkaline phosphatase =\< IULN * Any ethnic group * Prior therapy is allowed if \>= 4 weeks prior to registration * Life expectancy of at least 6 months * Ability to understand and the willingness to sign a written informed consent document * Willingness to comply with oral home treatment and visit schedule * Patients with reproductive capacity must be willing to use adequate contraception (barrier contraception, birth control pills, or other highly effective hormonal agents) or abstain from sexual activity for the duration of the study and 30 days beyond the end of therapy Exclusion Criteria: * Pregnant women * Breastfeeding women * Confirmed symptomatic multiple myeloma (MM), defined by any of the following: * Lytic lesions on skeletal survey * Anemia attributable to plasma cell infiltrate in marrow * Hypercalcemia * Renal dysfunction not attributable to other causes * Uncontrolled intercurrent illness, including but not limited to active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, psychiatric illness or social situations that would compromise compliance with study medication or follow up visits * Patients with high predisposition to gastrointestinal bleeding, such as known gastroesophageal varices or active peptic ulcer disease * Patients with chronic liver disease (such as hepatitis B, hepatitis C, or alcoholic cirrhosis) * Prior daily ingestion of green tea or green tea extract within 6 months of study entry * Patients who have previously experienced any adverse symptoms related to green tea or any of the inactive components present in Polyphenon E capsules * Concurrent use of investigational or commercial agent or therapy with the intent to treat MGUS and/or SMM