Brief Summary: This phase I trial tests the safety, side effects studies chemotherapy followed by chemotherapy at the same time as radiation therapy (chemoradiation) before surgery (neoadjuvant) in treating patients with stage gastric (stomach) or gastroesophageal junction cancer . Chemotherapy drugs, such as docetaxel, oxaliplatin , leucovorin, fluorouracil, and capecitabine, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Giving chemotherapy and chemoradiation before surgery may make the tumor smaller and may reduce the amount of normal tissue that needs to be removed.

Detailed Description: PRIMARY OBJECTIVES: I. To evaluate the feasibility of delivering tailored targeted neoadjuvant therapy with chemotherapy followed by chemoradiation and surgery in patients with gastroesophageal junction gastroesophageal junction (GEJ) and gastric cancer. II. To assess the toxicity of delivering tailored targeted neoadjuvant therapy with chemotherapy followed by chemoradiation and surgery in patients with GEJ and gastric cancer. SECONDARY OBJECTIVES: I. To identify the resident microbiota species associated with higher response to the combination therapy and quantify abundance and diversity of favorable bacterial communities over the course of the therapy. II. To evaluate local control, progression-free survival, and overall survival at 3, 6, 9, 12 and 24 months after treatment with neoadjuvant chemotherapy and chemoradiation. III. To describe the perfusion and early tumor uptake kinetics of primary tumor targets at baseline, during and following systemic chemotherapy and chemoradiation therapies using 18F-fluorodeoxyglucose (18F-FDG) digital photon counting positron emission tomography/computed tomography (dPET/CT) approaches. IV. To evaluate 18F-FDG dPET/CT to evaluate and characterize residual primary tumor following neoadjuvant chemotherapy and initial chemoradiation therapy for subsequent adaptive boost radiation delivery. EXPLORATORY OBJECTIVE : I. To explore FDG dPET standardized uptake value (SUV) metrics (e.g., SUVmax, SUVpeak, SUVmax Tumor-to-Liver, SUVpeak Tumor-to-Liver, metabolic tumor volume, etc.) on early dynamic PET perfusion, early tumor FDG uptake and delayed tumor FDG uptake to better predict pathologic response of primary tumor following multimodality therapy and surgical resection. OUTLINE: NEOADJUVANT CHEMOTHERAPY: Patients receive FLOT chemotherapy consisting of docetaxel intravenously (IV) , oxaliplatin IV, leucovorin IV, and fluorouracil IV over 24 hours on day 1 or FOLFOX chemotherapy consisting of oxaliplatin IV and leucovorin IV, and fluorouracil IV continuously over 24 hours on days 1 and 2. Treatment repeats every 2 weeks for 4 cycles in the absence of disease progression or unacceptable toxicity. NEOADJUVANT CHEMORADIATION: Within 4 weeks after completing neoadjuvant chemotherapy, patients undergo radiation therapy in 25 fractions over 5 weeks. Patients also receive either fluorouracil IV continuously for 24 hours on days 1-5 or capecitabine orally (PO) twice daily (BID) on days 1-5. Cycles repeat weekly for 5 weeks in the absence of disease progression or unacceptable toxicity. SURGERY: Within 4-8 weeks after neoadjuvant chemoradiation, patients undergo surgical resection according to tumor location and per surgeon expertise. After completion of study treatment, patients are followed up for 24 months.