A Study to Evaluate Safety, Tolerability, and Efficacy Profile of Rivoceranib With Paclitaxel in Advanced Gastric or Gastroesophageal Junction Cancer

Inclusion Criteria 1. Participants with documented locally advanced unresectable or metastatic gastric or gastroesophageal junction cancer refractory to or relapsing after first line platinum and fluoropyrimidine containing chemotherapy (with or without trastuzumab) with an indication for therapy with paclitaxel and an antiangiogenic agent. If disease progression occurs during or within 6 months after completion of any adjuvant chemotherapy, this therapy is considered a first-line chemotherapy for participant eligibility. 2. Participants who have provided tumor tissue prior to initiation of first-line therapy and have provided or can provide tumor tissue prior to screening in this study. This will be optional for Phase I participants. Tumor tissue must not have been irradiated. 3. Participants who have at least 1 measurable lesion as defined by RECIST v1.1. This will be optional for Phase I participants. 4. Adequate bone marrow, renal, and liver function evidenced by: 1. Hematologic: Absolute neutrophil count of ≥1,500/cubic millimeter (mm\^3), platelet count of ≥ 1,00,000/mm \^3, and hemoglobin of ≥9.0 grams (g)/deciliter (dL). Transfusion of platelets or red blood cells to meet the inclusion criteria within 2 weeks of screening is not allowed. 2. Adequate renal function, defined as meeting any 1 of the following criteria: i. Serum creatinine \<1.5 × upper limit of normal (ULN). ii. Creatinine clearance based on the Cockcroft-Gault estimate ≥50 milliliters per minute (mL/min) or creatinine clearance based on urine collection (12 or 24 hours) ≥50 mL/min. iii. In addition, urinary protein should be \<2+ on dipstick or routine urinalysis. If urine dipstick or routine analysis indicates proteinuria ≥2+, then a 24 hour urine or urine protein/creatinine ratio must be collected and must demonstrate \<2 g of protein in 24 hours. c) Hepatic: Serum bilirubin \<1.5 × ULN, aspartate and alanine aminotransferase ≤3.0 × ULN (≤5.0 × UNL, if with liver metastases). If liver and/or bone metastases alkaline phosphatase ≤5 × ULN. 5. Blood coagulation tests: Prothrombin time and international normalized ratio ≤1.5 × ULN. 6. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1. 7. Estimated life expectancy of at least 12 weeks. 8. Ability to swallow the study drug without chewing, breaking, crushing, opening or otherwise altering the product formulation. If vomiting occurs, the dose will not be replaced. Antiemetics must be used at efficacious doses. 9. No major gastrointestinal disease (e.g., chronic diarrheal disease) or intestinal surgery that can jeopardize drug absorption. Exclusion Criteria 1. Prior use of taxane (paclitaxel or docetaxel) or any contraindication for therapy with paclitaxel. 2. Previous treatment with rivoceranib or any other systemic therapy with a vascular endothelial growth factor (VEGF) pathway inhibitor. 3. Known hypersensitivity to rivoceranib or any component of its formulation or history of severe adverse events, including uncontrolled hypertension or other common anti-angiogenesis drug class effects during prior exposure to vascular inhibitors. 4. Any unresolved toxicity Grade \>1 (except alopecia) from previous anticancer therapy (including radiotherapy). 5. Has history of another malignancy within 2 years prior to screening. Participants with the following are eligible for this study if, in the opinion of the investigator, they do not pose a significant risk to life expectancy: 1. Bladder tumors considered superficial such as noninvasive (T1a) and carcinoma in situ (Tis). 2. Curatively treated cervical carcinoma in situ. 3. Thyroid papillary cancer with prior treatment. 4. Carcinoma of the skin without melanomatous features. 5. Prostate cancer which has been surgically or medically treated and not likely to recur within 2 years. 6. Known brain metastasis or other central nervous system metastasis that is either symptomatic or untreated. Metastases that have been treated by complete resection and/or radiotherapy demonstrating stability or improvement are not an exclusion criterion provided they are stable as shown by computed tomographic scan at least 4 weeks before screening without evidence of cerebral edema. Participants on stable dose of corticosteroids or anticonvulsants are permitted. 7. Has received prior anticancer therapy within 3 weeks before Cycle 1 Day 1. Traditional herbal remedies with anti-infective, immune stimulating, or anticancer properties are not allowed from screening throughout the entire period of study participation. 8. Current or recent (within 10 days of Cycle 1 Day 1) use of full dose oral or parenteral anticoagulants or other thrombolytic agents for therapeutic (as opposed to prophylactic) purposes, clinically serious non-healing wounds, or incompletely healed bone fracture. A maximum dose of 325 milligrams (mg)/day of aspirin is allowed. 9. Participants who had therapeutic paracentesis of ascites (\>1 liter \[L\]) within the 2 months prior to starting study treatment or who, in the opinion of the investigator, will likely need therapeutic paracentesis of ascites (\>1L) within 2 months of Cycle 1 Day 1. 10. Concomitant treatment with strong inhibitors or inducers of CYP3A4, CYP2C9, and CYP2C19. 11. Active bacterial infections (including tuberculosis and syphilis) requiring systemic antibiotic therapy. 12. Known history of human immunodeficiency virus infection. 13. Active hepatitis B or C infection or chronic hepatitis B or C infection requiring treatment with antiviral therapy or prophylactic antiviral therapy; unless evidence of viral suppression has been documented and the participant will remain on appropriate antiviral therapy throughout the study. 14. Child-Pugh Stage B and C liver function impairment. 15. Pregnant or breastfeeding women. Participants unwilling to comply with birth control requirements will not be eligible. 16. History of uncontrolled hypertension (blood pressure ≥140/90 mmHg and change in antihypertensive medication within 7 days prior to screening) that is not well managed by medication and the risk of which may be precipitated by a VEGF inhibitor therapy. History of hypertensive crisis, and hypertensive encephalopathy. 17. Participants who have a known history of symptomatic congestive heart failure (New York Heart Association III to IV), symptomatic or poorly controlled cardiac arrhythmia, complete left bundle branch block, bifascicular block, or any clinically significant ST segment and/or T wave abnormalities, corrected QT interval by Fredericia (QTcF) \> 450 msec for males or QTcF \> 470 milliseconds (msec) for females prior to screening. 18. History of bleeding diathesis or clinically significant bleeding within 14 days prior to Cycle 1 Day 1. This includes a history of gastrointestinal bleeding, gastric stress ulcerations, or peptic ulcer disease within the past 3 months prior to Cycle 1 Day 1 that, in the investigator's opinion, may place the participant at risk of side effects from anti-angiogenesis products. 19. History of clinically significant thrombosis (bleeding or clotting disorder) within the past 3 months prior to Cycle 1 Day 1 that, in the investigator's opinion, may place the participant at risk of side effects from anti-angiogenesis products. 20. History of other significant cardiovascular diseases or vascular diseases within the last 6 months prior to screening (e.g., myocardial infarction or unstable angina pectoris, stroke or transient ischemic attack, or significant peripheral vascular diseases) that, in the investigator's opinion, may pose a risk to the participant on vascular endothelial growth factor receptors (VEGFR) inhibitor therapy. 21. History of clinically significant glomerulonephritis, biopsy-proven tubulointerstitial nephritis, crystal nephropathy, or other renal insufficiencies. 22. Psychological, familial, sociological, or geographical conditions including drug or alcohol abuse that do not permit compliance with the study participation or evaluation of the study results.