Nab-Paclitaxel PIPAC in Combination With Paclitaxel and Ramucirumab for the Treatment of Stomach Cancer With Peritoneal Metastases

Inclusion Criteria: * Patients must have failed first-line systemic therapy (fluorouracil, leucovorin calcium, oxaliplatin \[FOLFOX\] with or without immunotherapy, or other fluoropyrimidine and platinum-based therapy) * Prior immunotherapy allowed * Up to 4 cycles of second-line therapy allowed if no progression is documented * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Histologically or cytologically confirmed gastric adenocarcinoma * Visible peritoneal metastatic disease on cross-sectional imaging or diagnostic laparoscopy (does not have to be measurable by RECIST 1.1) * Fully recovered from acute toxic effects (except alopecia, hearing loss, or non-clinically significant laboratory abnormalities) ≤ grade 1 of prior anti-cancer therapy * The patient's urinary protein is ≤ 1+ 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 \< 1000mg protein in 24 hours * Complete medical history and physical exam (within 28 days prior to day 1 of protocol therapy) * Absolute neutrophil count (ANC) ≥ 1,500/mcL (within 28 days prior to day 1 of protocol therapy) * Platelets ≥ 100,000/mcL (within 28 days prior to day 1 of protocol therapy) * Hemoglobin ≥ 8 g/dL (within 28 days prior to day 1 of protocol therapy) * Serum albumin ≥ 2.8 g/dL (within 28 days prior to day 1 of protocol therapy) * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (unless has Gilbert's disease, then direct bilirubin \< 1.5 mg/dL) (within 28 days prior to day 1 of protocol therapy) * Aspartate aminotransferase (AST) ≤ 5 x ULN (within 28 days prior to day 1 of protocol therapy) * Alanine aminotransferase (ALT) ≤ 5 x ULN (within 28 days prior to day 1 of protocol therapy) * International normalized ratio (INR) ≤ 1.5 x ULN (within 28 days prior to day 1 of protocol therapy) * Prothrombin time (PT) ≤ 1.5 x ULN (within 28 days prior to day 1 of protocol therapy) * Partial thromboplastin time (PTT) ≤ 1.5 x ULN (within 28 days prior to day 1 of protocol therapy) * Calculated creatinine clearance of ≥ 45 mL/min per 24 hour urine test or the Cockcroft-Gault formula (within 28 days prior to day 1 of protocol therapy) * Seronegative for HIV antigen (Ag)/antibody (Ab) combo (within 28 days prior to day 1 of protocol therapy) * If seropositive, patient may be eligible if they are stable on antiretroviral therapy, have a CD4 T cell count ≥ 200/µL, and have an undetectable viral load * Documented virology status of hepatitis, confirmed by hepatitis B virus (HBV) and hepatitis C virus (HCV) tests (within 28 days prior to day 1 of protocol therapy) * For patients with active HBV, HBV deoxyribonucleic acid (DNA) \< 500 IU/mL during screening, initiation of anti-HBV treatment at least 14 days prior to day 1 of cycle 1, and willingness to continue anti-HBV treatment during the study (per standard of care) * If seropositive for HCV, nucleic acid quantification must be performed. Viral load must be undetectable * WOMEN OF CHILDBEARING POTENTIAL (WOCBP): Negative urine or serum pregnancy test (within 28 days prior to day 1 of protocol therapy) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control (e.g., licensed hormonal/barrier methods or surgery intended to prevent pregnancy \[or with a side effect of pregnancy prevention\]) or abstain from heterosexual activity for the course of the study through at least 14 months after the last dose of protocol therapy. * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Intolerance to taxanes * Bowel obstruction requiring exclusive total parenteral nutrition * Any history of, or current, brain or subdural metastases * Life expectancy \< 3 months * Treatment with therapeutic oral or IV antibiotics within 14 days prior to day 1 cycle 1 of treatment * Patients receiving prophylactic antibiotics are eligible, provided the signs of active infection have resolved * Any prior malignancy except adequately treated basal or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease-free for two years * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents (taxanes, etc.) * Clinically significant uncontrolled illness such as uncontrolled hypertension (HTN) * History of arterial thromboembolic events such as myocardial infarction (MI), cerebrovascular accident (CVA) * History of gastrointestinal (GI) perforation * FEMALES ONLY: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)