Ixazomib Citrate With Gemcitabine Hydrochloride and Doxorubicin Hydrochloride in Treating Patients With Urothelial Cancer That is Metastatic or Cannot Be Removed by Surgery

Platelet count of \< 100 x 10\^9/L; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment

An absolute neutrophil count of \< 1.0 x 10\^9/L

A calculated creatinine clearance of \< 30 mL/min using Cockcroft Gault or measured by 24 hour urine

Patient has \>= grade 3 peripheral neuropathy, or grade 2 with pain on clinical examination during the screening period

Total bilirubin \>= 1.5 x the upper limit of the normal range (ULN)

Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent

Female subject is pregnant or breast-feeding

* Confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (beta-hCG) pregnancy test (unless there is reasonable certainty that beta-hCG is coming from the tumor); pregnancy testing is not required for post-menopausal or surgically sterilized women

Participation in other clinical trials with investigational agents not included in this trial, within 30 days of the start of this trial and throughout the duration of this trial

Patients with significant atherosclerotic disease, as defined by:

* Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) class III or IV heart failure uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities

* Symptomatic congestive heart failure

* Claudication limiting activity and

* History of cerebrovascular events within the last year (including transient ischemic attack \[TIA\])

* Unstable angina

Patients with known active brain metastases; (subjects with previously treated brain metastases are eligible provided they are stable \[defined as without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment\] and neurologic symptoms have returned to baseline)

Radiotherapy within 28 days before enrollment; if the involved field is small, 14 days will be considered a sufficient interval between treatment and administration of the therapy

Diagnosed or treated for another malignancy within 2 years before study enrollment or previously diagnosed with another malignancy and have any evidence of residual disease; patients with pathologically confirmed completely resected prostate cancer no higher than stage pT2a and no biochemical relapse, or pT2c tumors involving less than 5% of the prostate and no biochemical relapse, nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection

Systemic treatment, within 14 days before the first dose of ixazomib, with strong inhibitors of cytochrome P450, family 1, subfamily A, polypeptide 2 (CYP1A2) (fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of cytochrome P450, family 3, subfamily A (CYP3A) (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole, nefazodone, posaconazole) or strong CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of Ginkgo biloba or St. John's wort

Failure to have fully recovered (ie, =\< grade 1 toxicity) from the reversible effects of prior chemotherapy

Major surgery within 14 days before enrollment; the PI will serve as the final arbiter as to what constitutes major surgery

Infection requiring current intravenous antibiotic therapy; the PI will serve as the final arbiter regarding eligibility

Ongoing or active systemic infection, known active hepatitis B or C virus infection, or known human immunodeficiency virus (HIV) positive

Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol

Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib including difficulty swallowing; patients who have had cystectomy with conduit, neobladder, or pouch using a portion of their terminal ileum are allowed if, the patient is stable without clinically significant metabolic disturbances OR stoma- and/or anastomosis-related complications OR post-surgical gut abnormalities that would compromise drug absorption

What this study is about