Inclusion Criteria:  Male and female patients, age ≥18 years at time of signing informed written consent Confirmed diagnosis of diffuse cutaneous systemic sclerosis/scleroderma Disease duration not longer than 60 months defined as the time from the first non-Raynaud phenomenon manifestation Scleroderma skin thickness score (modified Rodnan skin score) between 15 and 45 Evidence of scleroderma-related lung involvement on chest CT scan completed within the preceding 3 months or at screening study visit Pulmonary function testing demonstrating FVC ≥45% predicted and DLCO ≥40% predicted at screening study visit Resting transthoracic echocardiogram within the preceding 6 months or at screening study visit without evidence of pulmonary artery hypertension Stable mycophenolate dose during the preceding 3 months for those who are taking mycophenolate. Mycophenolate use is not an eligibility requirement to participate; but those participants already using mycophenolate at screening study visit will continue taking the medication throughout the entire study. Willingness to undergo supervised withdrawal during the first 90 days of the study of any other medication besides mycophenolate used specifically as treatment of scleroderma-related interstitial lung disease with confirmed stable pulmonary status. Willingness to undergo supervised withdrawal during the first 90 days of the study of any other prohibited medications with confirmed stable status. Able to understand and sign a written informed consent form Able to understand the importance of adhering to study treatment and the study protocol, and willing and able to follow all study requirements, including the concomitant medication restrictions, throughout the study Practice birth control requirements for sexually active female participants including option of abstinence for the entire study and for at least 90 days after the last dose of study medication Practice birth control requirements for sexually active male participants or partners including option of abstinence for the entire study and for at least 90 days after the last dose of study medication  Exclusion Criteria:  Pulmonary artery hypertension under treatment Evidence of clinically significant pulmonary hypertension or left ventricular dysfunction with left ventricular ejection fraction < 40% from either prior heart catheterization or resting transthoracic echocardiography within the preceding 6 months. Evidence of significant gastrointestinal involvement by scleroderma as assessed by the University of California, Los Angeles, Scleroderma Clinical Trial Consortium Gastrointestinal Tract multi-item questionnaire, 2.0 ([UCLA SCTC GIT 2.0) at screening study visit. Known esophageal stricture sufficient to limit the ability to swallow oral medication Prior history of scleroderma renal crisis Another connective-tissue disorder (eg, rheumatoid arthritis, systemic lupus erythematosus) Any other significant pulmonary disorder (e.g., chronic obstructive pulmonary disease, emphysema, adult moderate to severe asthma) Significant environmental exposure known to cause pulmonary fibrosis including, but not limited to, drugs (e.g., amiodarone), asbestos, beryllium, radiation, or domestic birds or other exposures associated with hypersensitivity pneumonitis Unstable or deteriorating cardiac disease within the preceding 6 months including but not limited to unstable angina pectoris, myocardial infarction (heart attack), heart failure requiring hospitalization, poorly controlled heart arrhythmia, or significant pericardial effusion/fluid collection around the heart Known liver disease (e.g., chronic hepatitis or cirrhosis) Significant abnormality of liver function tests Significant kidney function impairment of any cause as evidenced by creatinine clearance <30 mL/min Known active or suspected peptic (stomach) ulcer Known active hematologic blood-related disorder other than anemia of chronic disease or iron deficiency anemia Significant abnormality of blood count including hemoglobin ≤ 8.0 gm/dl, absolute neutrophil count ≤ 1000, or platelet count ≤ 75,000 Known hematologic blood-related malignancy Prior stem cell or bone marrow transplant History of any malignancy within the last 5 years other than non-melanoma skin cell cancer cured by local resection or a carcinoma-in-situ Any condition likely to result in death within 12 months. Any condition which might be significantly worsened by the known side effects associated with ixazomib including known ≥ grade 2 peripheral neuropathy Tobacco smoking within 3 months of screening study visit or unwillingness to avoid smoking throughout the study (e.g., cigarette, pipe, or cigar) History of alcohol or substance abuse in the previous 2 years Any active infection including, but not limited to, bronchitis, pneumonia, sinusitis, or urinary tract infection Pregnancy or lactation/breast feeding Expectation of study participation being interrupted on account of a foreseeable medical or surgical event Prior use of ixazomib or other proteasome inhibitor medication Suspected intolerance, allergy, or hypersensitivity to ixazomib or any of its excipients Any prior use of rituximab Any prior use of cyclophosphamide Ongoing use within the preceding 28 days or expected use of an investigational drug (an investigational drug is defined as any drug that has not been FDA approved for marketing) Ongoing use or expected use of any of the following therapies: Strong inducers of a cytochrome drug metabolizing enzyme in the liver (CYP3A ). (e.g. rifampin, rifapentine, rifabutin, carbamazepine, enzalutamide, phenytoin, fosphenytoin, phenobarbital, St. John's wort) Ongoing use or expected use of any of the following medications: cyclophosphamide, rituximab, abatacept, nintedanib, tocilizumab, intravenous immunoglobulin (IVIG), methotrexate, leflunomide, azathioprine, sirolimus, tacrolimus, oral corticosteroids at a dose >10 mg/d prednisone equivalent, D-penicillamine, minocycline, interferon-γ, bosentan, ambrisentan, macitentan, phosphodiesterase inhibitors (sildenafil or tadalafil for uses other than erectile dysfunction or Raynaud phenomenon), riociguat, tumor necrosis factor-α (TNF-α) inhibitors (infliximab, etanercept, adalimumab, certolizumab, golimumab), and cyclosporine, .