Inclusion Criteria:

   - Males and females ≥ 18 years of age

   - Histologically-proven AL amyloidosis, confirmed by positive Congo red stain with green
   birefringence on polarized light microscopy with evidence of measurable clonal disease
   that requires active treatment as defined below:

   - Patients must have clonal disease measureable by serum free light chain (FreeliteTM)
   assay:

      - For the dose-escalation cohort: this is defined as having any elevation in the
      amyloidogenic (i.e. clonal) light chain with an abnormal free kappa:lambda ratio

      - For the dose expansion cohorts: in addition to the above, there must be a
      difference between the amyloidogenic (i.e. clonal) and non-amyloidogenic light
      chain (dFLC) of at least 50mg/L (5mg/dL)

   - Relapsed (progressed after prior response) or refractory (failed to achieve at least a
   partial response) to at least one prior therapy for amyloidosis.

      - Patients that received an autologous stem cell transplant must be at least 3
      months post-transplant and recovered from acute transplant-related toxicities.

      - Patients that were unable to tolerate at least 1 cycle of an alkylating agent
      plus corticosteroid (e.g. melphalan + dexamethasone) or alternative prior regimen
      because of severe adverse events (e.g. hypersensitivity reaction) may be
      considered after discussion with the study PI/Medical Monitor.

   - Objective, measureable, symptomatic organ involvement, defined as one or more of the
   following:

      - Kidney: albuminuria ≥ 500 mg/day in a 24-hour urine specimen

      - Heart: presence of mean left ventricular wall thickness on echocardiogram greater
      than 12 mm in the absence of hypertension or valvular heart disease, or
      unexplained low voltage (< 0.5 mV) on ECG, or NT-proBNP > 332 ng/L in the absence
      of impaired renal function [estimated glomerular filtration rate (eGFR) < 45
      mL/min]

      - Liver: hepatomegaly on physical exam with elevated alkaline phosphatase > 1.5 x
      ULN

      - GI Tract: biopsy showing amyloid deposition along with symptoms such as GI
      bleeding or persistent diarrhea (> 4 loose stools/day) Autonomic or Peripheral
      Nervous System: defined as orthostasis, symptoms of nausea or dysgeusia,
      recurrent diarrhea or constipation, abnormal sensory and/or motor findings on
      neurologic exam, or gastric atony by gastric emptying scan

      - Note: Skin, lymph node, or soft tissue involvement; carpal tunnel syndrome; or
      bone marrow amyloid as the sole clinical manifestations of amyloidosis are not
      sufficient for inclusion.

   - Amyloid cardiac biomarker stage I or II disease Staging defined by NT-proBNP and
   troponin T cut-offs of < 332 pg/mL and <0.035 ng/mL, respectively, as thresholds:
   Stage I, both under threshold; and Stage II, either troponin or NT-proBNP (but not
   both) over threshold. If troponin T is not available at local institution, troponin I
   may be used, but threshold is <0.1 ng/mL.23

   - Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-2

   - Clinical laboratory values as specified within 14 days of treatment:

      - Absolute neutrophil count (ANC) ≥ 1.0 x 109/L

      - Hemoglobin ≥8 g/dL [transfusion permitted]

      - Platelet count ≥75.0 x 109/L

      - Total bilirubin ≤ 2 x Upper Limit of Normal (ULN)

      - Alkaline phosphatase ≤ 5 x ULN

      - Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3.5 x ULN

      - CrCl ≥ 30 mL/min as measured by 24-hour urine

      - Screening ANC should be independent of granulocyte-and granulocyte/macrophage
      colony stimulating factor (G-CSF and GM-CSF) support for at least 1 week and of
      pegylated G-CSF for at least 2 weeks

      - Screening platelet count should be independent of platelet transfusions for at
      least 2 weeks

   - Written informed consent in accordance with federal, local, and institutional
   guidelines

   - Females of childbearing potential must agree to ongoing pregnancy testing and to
   practice contraception or abstain from heterosexual intercourse

   - Male patients must agree to practice contraception or to abstain from heterosexual
   intercourse

   - Male patients must agree not to donate semen or sperm

   - Life expectancy of ≥ 3 months

Exclusion Criteria:

   - Pregnant or lactating females

   - Major surgery within 21 days prior to first dose

   - Acute active infection requiring systemic antibiotics, antivirals, or antifungals
   within 14 days prior to first dose

   - Treatment with an experimental drug within 28 days of first dose

   - Active Human Immunodeficiency Virus (HIV) or hepatitis B or C infection

   - Bone marrow plasma cells ≥ 30% or clinical manifestations of multiple myeloma, such as
   hypercalcemia or lytic bone lesions

   - Cardiac exclusions:

      - Left ventricular ejection fraction (LVEF) < 40%

      - Amyloid cardiac biomarker stage III disease, defined as both NT-proBNP ≥ 332
      pg/mL and troponin T ≥ 0.035 ng/mL. If troponin T is not available at local
      institution, troponin I may be used, but cut-off is ≥ 0.1 ng/mL

      - New York Heart Association (NYHA) classification III or IV heart failure (see
      Appendix G) despite medical management

      - Unstable angina or myocardial infarction within 6 months prior to first dose

      - Grade 2 or 3 atrioventricular (AV) block (Mobitz type I is permitted) or sick
      sinus syndrome, unless subject has a pacemaker

      - Known history of sustained (> 30 second) ventricular tachycardia or cardiac
      syncope. Known history of recurrent non-sustained ventricular tachycardia (> 3
      beats) despite anti-arrhythmic therapy

      - Supine systolic blood pressure < 90 mm Hg, or symptomatic orthostatic
      hypotension, or a decrease in systolic blood pressure upon standing of > 20 mm Hg
      despite medical management (e.g. midodrine, fludrocortisones)

   - Significant peripheral neuropathy (Grade 3, Grade 4, or Grade 2 with pain) within 14
   days prior to first dose

   - Severe diarrhea (≥ grade 3) not controllable with medication or that requires total
   parenteral nutrition

   - History of bleeding diathesis, known factor X deficiency (level < 20%), or requirement
   for therapeutic anticoagulation with warfarin

   - Known allergies to carfilzomib or Captisol® (a cyclodextrin derivative used to
   solubilize carfilzomib)

   - Presence of other active malignancy with the exception of non-melanoma skin cancer,
   cervical cancer, treated early-stage prostate cancer provided that prostate-specific
   antigen is within normal limits, or any completely resected carcinoma in situ

   - Serious psychiatric or medical conditions that could interfere with treatment

   - Contraindication to any of the required concomitant drugs, including antiviral (e.g.
   Valacyclovir)

   - Patients in whom the required program of oral and IV fluid hydration is
   contraindicated, e.g. due to severe pre-existing pulmonary, cardiac, or renal
   impairment

   - Subjects with pleural effusions requiring thoracentesis or ascites requiring
   paracentesis within 14 days prior to first dose.