Futibatinib in Combination With Durvalumab Prior to Cystectomy for the Treatment of Muscle-Invasive Bladder Cancer Patients Who Are Ineligible for Cisplatin-based Therapy

Inclusion Criteria:

* Able to provide signed informed consent
* Female or male subjects \>= 18 years old
* Bodyweight \>30kg
* FGFR1, 2, or 3 overexpression as defined by a score of 3+ or 4+ on ribonucleic acid (RNA) in-situ hybridization (RNAScope assay)
* Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2
* Histologically confirmed urothelial carcinoma of the bladder

  * Mixed histologies are permitted if urothelial carcinoma is the predominant histology ( \>= 50%)
* Clinical stage T2-T4a, N0, M0 disease by trans urethral removal of bladder tumour (TURBT) and imaging studies (stage II-IIIA per American Joint Committee on Cancer \[AJCC\] 2018)
* Refuse or ineligible for cisplatin-based neoadjuvant chemotherapy as defined by any of the following:

  * ECOG performance status (PS) \> 1
  * Creatinine clearance (calculated or measured) \< 60 mL/min as measured by the Cockcroft-Gault formula
  * Common Terminology Criteria for Adverse Events version 5.0 (CTCAE v 5.0) grade \>= 2 hearing loss
  * CTCAE v 5.0 grade \>= 2 neuropathy
  * New York Heart Association (NYHA) class \> II cardiac dysfunction
* Treatment with anti-PD-1/PD-L1 therapy for non-muscle invasive bladder cancer (NMIBC) is permitted if it is completed \> 3 months before registration
* Eligible for radical cystectomy by the following:

  * Fit and planned for radical cystectomy according to local guidelines
* Archival transurethral resection of bladder tumor (TURBT) tissue submission must be 30 unstained slides. If archival tissue is unavailable, the patient must undergo cystoscopy and biopsy. The tumor sample must contain at least 20% viable tumor
* Evidence of post-menopausal status or negative urinary or serum pregnancy test for female premenopausal patients.
* Female subjects of childbearing potential and male subjects must be willing to completely abstain or agree to use a highly effective method of contraception (i.e., less than 1% failure rate), from the time of signing informed consent and for the duration of study participation through 90 days following the last dose of study drug.
* Hemoglobin \>= 9.0 g/dL
* Absolute neutrophil count (ANC) \> 1500 per mm\^3
* Platelet count \>= 100 x 10\^9/L
* International normalized ratio (INR) or activated partial thromboplastin time (aPTT) \< 1.5 × upper limit of normal (ULN), unless the patient is receiving anticoagulation therapy provided INR or PTT is within the therapeutic range of the intended anticoagulant therapy
* Serum bilirubin =\< 1.5 x institutional upper limit of normal (ULN)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal
* Phosphorus ≤ institutional upper limit of normal (ULN)
* Measured creatinine clearance (CL) \> 30 mL/min or calculated creatinine CL \> 30 mL/min by the Cockcroft-Gault formula or by 24-hour urine collection for determination of creatinine clearance
* Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up.
* Must have a life expectancy of at least 12 weeks

Exclusion Criteria:

* Women who are pregnant or breastfeeding
* Male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of durvalumab monotherapy
* Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks before the first dose of trial treatment
* Has upper tract urothelial carcinoma
* Has small-cell carcinoma component on histology
* Evidence of measurable nodal or metastatic disease
* Concurrent anticancer therapy (e.g., chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, hormonal therapy, investigational therapy, intravesical therapy, or tumor embolization)
* Received prior systemic chemotherapy for muscle-invasive bladder cancer at any time in the patient's medical history
* Has received anti-PD-1/PD-L1 therapy or FGFR inhibitor previously for MIBC, except if used in earlier stage urothelial carcinoma such as non-muscle invasive bladder cancer (NMIBC) and completed \> 3 months prior to registration

  * Must not have experienced a toxicity that led to permanent discontinuation of prior immunotherapy.
  * All AEs while receiving prior immunotherapy must have completely resolved or resolved to baseline prior to screening for this study.
  * Must not have experienced a ≥Grade 3 immune related AE or an immune related neurologic or ocular AE of any grade while receiving prior immunotherapy. NOTE: Patients with endocrine AE of ≤Grade 2 are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic.
  * Must not have required the use of additional immunosuppression other than corticosteroids for the management of an AE, not have experienced recurrence of an AE if re-challenged, and not currently require maintenance doses of \> 10 mg prednisone or equivalent per day.
* Underwent major surgery and has not recovered adequately from the intervention's toxicity and/or complications before starting therapy
* Has an active second malignancy except for low-risk localized prostate cancer on "watch and wait"
* Subjects with a history of malignancy that has been completely treated, with no evidence of active cancer for 2 years before enrollment, or subjects with surgically cured tumors with a low risk of recurrence are allowed to enroll at PI's discretion (e.g. adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease and effectively treated carcinoma in situ without evidence of disease).
* Has active cardiac disease, defined as:

  * Myocardial infarction or unstable angina pectoris within 3 months of the first date of study therapy
  * Unstable arrhythmias
  * Decompensated heart failure
  * Uncontrolled hypertension and unstable angina pectoris
  * Average QT corrected by the Fridericia formula (QTcF) \> 470 msec (males and females) (Note: If the QTcF is \> 470 msec in the first electrocardiography \[ECG\], a total of 3 ECGs separated by \>= 5 minutes should be performed. If the average of these 3 consecutive results for QTcF is =\< 470 msec, the subject meets eligibility in this regard.)
* Has any medical condition that may prevent the patient from undergoing radical cystectomy
* Must be at least 2 weeks beyond high-dose systemic corticosteroids; chronic steroid use up to 10 mg daily prednisone (or equivalent), intranasal, inhaled, topical steroids, local steroid injections (e.g., intra articular injection), steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication) are permitted
* Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc\]). The following are exceptions to this criterion:

  * Patients with vitiligo or alopecia
  * Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement
  * Any chronic skin condition that does not require systemic therapy
  * Patients without active disease in the last 5 years may be included but only after consultation with the study physician
  * Patients with celiac disease controlled by diet alone
* Has a known history of HIV-1/2 with detectable viral load and/or CD4 count \< 300/mL within the previous 3 months or active tuberculosis infection (clinical evaluation that may include clinical history, physical examination and radiographic findings, or tuberculosis testing in line with local practice).
* Has detectable hepatitis B virus (HBV) or hepatitis C virus (HCV) viral load polymerase chain reaction (PCR) if there is a known history of active hepatitis B or hepatitis C
* History and/or current evidence of significant ectopic mineralization/calcification including but not limited to the soft tissues, kidneys, intestines, myocardium, and lungs, except calcified lymph nodes and asymptomatic coronary calcification
* Current evidence of corneal or retinal disorder/ keratopathy including but not limited to bullous/ band keratopathy, corneal abrasion, inflammation/ulceration, keratoconjunctivitis etc., confirmed by ophthalmologic examination
* Have current evidence of endocrine alterations of calcium/phosphate homeostasis (e.g., parathyroid disorders, history of parathyroidectomy, tumor lysis, tumoral calcinosis) unless well controlled
* Have used drugs that are dual p-glycoprotein and strong CYP3A inducers or inhibitors within 7 days prior to the first dose of the study drug
* Has other concurrent medical or psychiatric conditions that, in the investigator's opinion, may be likely to confound study interpretation or prevent completion of the study procedure and follow-up examinations
* Known allergy or hypersensitivity to study drugs or any excipient.
* Receipt of live attenuated vaccine within 30 days prior to the first dose of investigational product (IP). Note: Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to 90days after the last dose of IP.
* Has other uncontrolled illnesses, ongoing or active infection, or serious chronic gastrointestinal conditions associated with diarrhea
* Any unresolved toxicity NCI CTCAE Grade ≥2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria

  * Patients with Grade ≥2 neuropathy will be evaluated on a case-by-case basis after consultation with the Study Physician.
  * Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab may be included only after consultation with the Study Physician
* History of allogenic organ transplantation