Testing JNJ-42756493 In Combination With Dexamethasone in Multiple Myeloma That Came Back After a Period of Improvement

Inclusion Criteria:

* A diagnosis of MM and documentation of at least 1 prior line of therapy including proteasome and immunomodulatory agents.
* Documented lab results confirming FGFR3 expression and mutational status determined by a clinical grade, next generation sequencing platform approved by the Sponsor-Investigator, the results of which must be obtained prior to registration.
* Patients with measurable disease by laboratory studies for determining eligibility must be obtained within 28 days prior to start of study drug):
* Must have an Eastern Cooperative Oncology Group (ECOG) performance status score 0, 1, or 2.
* Negative pregnancy status in women of childbearing potential must be confirmed within 7 days prior to start of study drug. Participants must use medically acceptable methods of birth control before the study entry, during the study, and until 3 months after taking the last dose of the study drug.
* Patient must sign the informed consent documents indicating that they understand the purpose of and procedures required for the study and are willing to participate in the study.
* Life Expectancy of ≥ 3 months.
* Able to take oral medications.
* Acceptable laboratory results must be met within 7 days of first study drug administration.

Exclusion Criteria:

* Patients in whom FGFR3 expression or mutational status cannot be determined.
* Chemotherapy, limited palliative radiotherapy or other anti-myeloma therapy within 14 days prior to the first dose of study drug. In addition, any treatment related toxicity should have recovered \< Grade 1 unless deemed to be irreversible.
* Patients who are receiving any other investigational agent.
* Patients with known CNS involvement, plasma cell leukemia or amyloidosis.
* Use of an investigational drug within 21 days or five-half-lives, whichever is shorter but not less than 14 days, preceding the first dose of study drug.
* History of allogeneic stem cell transplant.
* Autologous, peripheral stem cell transplant within 12 weeks of the first dose of study drug.
* Prior major surgical procedure or extensive radiation therapy within 4 weeks of the first dose of study treatment.
* Current use of corticosteroids, with the exception of inhaled or topical steroids.
* Previous or concurrent malignancies are allowed if it is clear that the patient is not symptomatic from the other tumor. The subject must not be receiving active therapy for the other tumor and the other tumor must be considered medically stable.
* Has a history of or current uncontrolled cardiovascular disease.
* Patients with evidence of mucosal or internal bleeding and/or platelet transfusion refractory. Patients cannot use growth factors within 7 days of start of study drug, or transfusion of blood or platelets within 7 days of start of study drug.
* Has impaired wound healing capacity defined as skin/decubitus ulcers, chronic leg ulcers, known gastric ulcers, or unhealed incisions.
* Serious psychiatric illness, active alcoholism, or drug addiction that may hinder or confuse follow-up evaluations.
* Any other condition that, in the Investigator's opinion, would contraindicate the patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures.
* Received prior FGFR inhibitor treatment or if the subject has known allergies, hypersensitivity, or intolerance to JNJ-42756493 or its excipients.
* Pregnant, breast feeding, or planning to become pregnant within 3 months after the last dose of study drug and males who plan to father a child while enrolled in this study or within 5 months after the last dose of study drug.
* Known HIV or active hepatitis B or C viral infection.
* History of cerebrovascular accident (CVA) within 6 months prior to registration.
* Gastrointestinal abnormalities, including bowel obstruction, inability to take oral medication, requirement for intravenous (IV) alimentation, active peptic ulcer or prior surgical procedures or bowel resection affecting absorption.
* Peripheral neuropathy ≥ Grade 2.
* Has persistent phosphate level \>ULN during screening (within 14 days of treatment and prior to Cycle 1 Day 1) despite medical management.
* Any corneal or retinal abnormality likely to increase the risk of eye toxicity.
* Patients that require the following prohibited therapy:

  1. Medicines known to have a risk of causing QTc prolongation and Torsades de Pointes
  2. Medications known to increase serum levels of phosphate and calcium
  3. Medications or substances known to be strong inhibitors or strong inducers of CYP3A4 or CYP2C9 before the recommended 5 half-life washout period