CAMPFIRE: A Study of Ramucirumab (LY3009806) in Children and Young Adults With Synovial Sarcoma

Inclusion Criteria: * Participants must have discontinued all previous treatments for cancer or investigational agents ≥7 days after the last dose or per the type of previous treatment as stated in the protocol and must have recovered from the acute effects to ≤Grade 2 for alopecia and decreased tendon reflex and to ≤Grade 1 for all other effects at the time of enrollment, unless otherwise noted. Consult with the Lilly clinical research physician or scientist for the appropriate length of time prior to the first dose of study treatment. * Participants with relapsed, recurrent, or refractory SS. * Participants must: * Have measurable disease by Response Evaluation Criteria in Solid Tumors, Version (RECIST) 1.1. * have received at least one prior line of systemic treatment (including neoadjuvant and adjuvant chemotherapy) that contains ifosfamide and/or doxorubicin, or any approved therapies for which they are eligible, unless the patient is not a suitable candidate for the approved therapy. * not be eligible for surgical resection at time of enrollment. * Adequate cardiac function, defined as: Shortening fraction of ≥27% by echocardiogram, or ejection fraction of ≥50% by gated radionuclide study. * Adequate blood pressure (BP) control, defined as: * Participants ≥18 years: Controlled hypertension defined as systolic BP ≤150 millimeters of mercury (mmHg) or diastolic BP ≤90 mmHg where standard medical management is permitted. Please note that ≥2 serial BP readings should be obtained and averaged to determine baseline BP. * Participants \<18 years: A BP ≤95th percentile for age, height, and gender measured as described in National High Blood Pressure Education Program Working Group (NHBPEPWG) on High Blood Pressure in Children and Adolescents (2004), where standard medical management is permitted. Please note that ≥2 serial BP readings should be obtained and averaged to determine baseline BP. * Adequate hematologic function, as defined as: * Absolute neutrophil count (ANC): ≥750/microliters (µL) granulocyte-colony stimulating factor (G-CSF) permitted up to 48 hours prior. Participants with documented history of benign ethnic neutropenia or other conditions could be considered with a lower ANC after discussion with and approval from the Lilly clinical research physician or scientist. * Platelets: ≥75,000/cubic millimeters. Platelet transfusion permitted up to 72 hours prior. * Hemoglobin: ≥8 grams per deciliter (g/dL) (≥80 g/liter). Transfusions to increase the participant's hemoglobin level to at least 8 g/dL are permitted; however, study treatment must not begin until 7 days after the transfusion, and complete blood count criteria for eligibility are confirmed within 24 hr of first study dose. * Adequate renal function, as defined as: * Creatinine clearance or radioscope glomerular filtration rate (GFR) ≥60 milliliters/minute/meters squared OR serum creatinine meeting the following parameters: * for participants ≥18 years of age serum creatinine ≤1.5×upper limit of normal (ULN); * for participants \<18 years of age, serum creatinine based on age/gender as follows: Age 1 to \<2 years maximum serum creatinine 0.6, Age 2 to \<6 years maximum serum creatinine 0.8, Age 6 to \<10 years maximum serum creatinine 1.0, Age 10 to \<13 years maximum serum creatinine 1.2, Age 13 to \<16 years maximum serum creatinine 1.5 for males and 1.4 for females, Age 16 to \<18 years maximum serum creatinine 1.7 for males and 1.4 for females. * Urine protein meeting the following parameters: * for participants ≥18 years of age: \<2+ on dipstick or routine urinalysis. If urine dipstick or routine analysis indicates proteinuria ≥2+, then a 24-hour urine must be collected and must demonstrate \<2 grams of protein in 24 hours to allow participation in the study. * for participants \<18 years of age: ≤30 milligrams per deciliter urine analysis or \<2+ on dipstick. If urine dipstick or routine analysis indicates proteinuria ≥2+, then a 24-hour urine must be collected and must demonstrate \<1 g of protein in 24 hours to allow participation in the study. * Adequate liver function: * Total bilirubin: ≤1.5×ULN. Except participants with document history of Gilbert Syndrome who must have a total bilirubin level of \<3.0×ULN. * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST): ≤2.5×ULN OR ≤5.0×ULN if the liver has tumor involvement. * The participant has an adequate coagulation function as defined by International Normalized Ratio ≤1.5 or prothrombin time ≤1.5×ULN, and partial thromboplastin time ≤1.5×ULN if not receiving anticoagulation therapy. For participants receiving anticoagulants, exceptions to these coagulation parameters are allowed if they are within the intended or expected range for their therapeutic use. Participants must have no history of clinically significant active bleeding (defined as within 14 days of first dose of study drug) or pathological condition that carries a high risk of bleeding (for example, tumor involving major vessels or known esophageal varices). * The participant has adequate hematologic and organ function ≤1 week (7 days) prior to first dose of study drug. * Female participants of childbearing potential must have a negative urine or serum pregnancy test within 7 days prior to randomization. Male and female participants must agree to use highly effective contraception for the duration of the study and up to 3 months following the last dose of ramucirumab and 6 months following the last dose of docetaxel and gemcitabine in order to prevent pregnancy. Exclusion Criteria: * Participants with severe and/or uncontrolled concurrent medical disease or psychiatric illness/social situation that in the opinion of the investigator could cause unacceptable safety risks or compromise compliance with the protocol. * Participants who have active infections requiring therapy. * Participants with an active fungal, bacterial, and/or known severe viral infection including, but not limited to, human immunodeficiency virus (HIV) or viral (A, B, or C) hepatitis (screening is not required). * Participants who have had allogeneic bone marrow or solid organ transplant are excluded. * Surgery: Participants who have had, or are planning to have, the following invasive procedures are not eligible: * Major surgical procedure, laparoscopic procedure, or significant traumatic injury within 28 days prior to enrollment. * Central line placement or subcutaneous port placement is not considered major surgery. * Core biopsy, fine needle aspirate, and bone marrow biopsy/aspirate are not considered major surgeries. * Surgical or other wounds must be adequately healed prior to enrollment. * Bleeding and thrombosis: * Participants with evidence of active bleeding or a history of significant (≥Grade 3) bleeding event within 3 months prior to enrollment are not eligible. * Participants with a bleeding diathesis or vasculitis are not eligible. * Participants with known or prior history in the prior 3 months of esophageal varices are not eligible. * Participants with a history of deep vein thrombosis requiring medical intervention (including pulmonary embolism) within 3 months prior to study enrollment are not eligible. * Participants with a history of hemoptysis or other signs of pulmonary hemorrhage within 3 months prior to study enrollment are not eligible. * Cardiac: * Participants with a history of central nervous system (CNS) arterial/venous thromboembolic events (VTEs) including transient ischemic attack (TIA) or cerebrovascular accident (CVA) within 6 months prior to study enrollment are not eligible. * Participants with myocardial infarction or unstable angina within the prior 6 months. * Participants with New York Heart Association Grade 2 or greater congestive heart failure (CHF). * Participants with serious and inadequately controlled cardiac arrhythmia. * Participants with significant vascular disease (eg, aortic aneurysm, history of aortic dissection). * Participants with clinically significant peripheral vascular disease. * Participants who have a history of fistula, gastrointestinal (GI) ulcer or perforation, or intra-abdominal abscess within 3 months of study enrollment are not eligible. * Participants with a history of hypertensive crisis or hypertensive encephalopathy within 6 months of study enrollment are not eligible. * Participants who have non-healing wound, unhealed or incompletely healed fracture, or a compound (open) bone fracture at the time of enrollment are not eligible. * Participants previously treated and progressed on combination gemcitabine and docetaxel regimen. Participants who received combination as maintenance therapy, without progression, would be eligible. * Participants with a known hypersensitivity to ramucirumab, gemcitabine, docetaxel, or agents formulated with Polysorbate 80. * Hepatic impairment: * Severe liver cirrhosis Child-Pugh Class B (or worse). * Cirrhosis with a history of hepatic encephalopathy. * Clinically meaningful ascites resulting from cirrhosis and requiring ongoing treatment with diuretics and/or paracentesis. * History of hepatorenal syndrome. * The participant has a bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection (eg, hemicolectomy or extensive small intestine resection with chronic diarrhea), Crohn's disease, ulcerative colitis, or chronic diarrhea. * The participant has symptomatic interstitial pneumonia or pulmonary fibrosis (or consistent findings of interstitial pneumonia/pulmonary fibrosis on imaging). * Participants with central nervous system (CNS) involvement are ineligible.