Ramucirumab and Paclitaxel or FOLFIRI in Advanced Small Bowel Cancers

Inclusion Criteria: * Patients must have histologically or cytologically confirmed small bowel adenocarcinoma. Ampullary adenocarcinomas are not eligible. Patients must have metastatic disease or locally advanced unresectable disease * Brain metastases are allowed if they have been adequately treated with radiotherapy or surgery and stable for at least 30 days prior to registration. Patients must be neurologically asymptomatic and without corticosteroid treatment for at least 7 days prior to registration * Patients must have measurable or non-measurable disease. All scans needed for assessment of measurable disease must be performed within 28 days prior to registration. Non-measurable disease must be assessed within 42 days prior to registration. All disease must be assessed and documented on the Baseline Tumor Assessment Form * Patients must have progressed on prior therapy with a fluoropyrimidine and/or oxaliplatin, given either for metastatic/locally advanced disease or as adjuvant therapy completed within the previous 12 months * Patients must have completed prior chemotherapy, immunotherapy, or radiation therapy at least 14 days prior to registration and all toxicity must be resolved to grade 1 (with the exception of grade 2 neuropathy) prior to registration. In Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 grade 2 sensory neuropathy is defined as "moderate symptoms; limiting instrumental activities of daily living (ADLs)" * Patients must have a complete medical history and physical exam within 28 days prior to registration * Patients must have a Zubrod performance status of 0 or 1 * Absolute neutrophil count (ANC) \>= 1,500/mcL (must be obtained within 28 days prior to registration) * Platelets \>= 100,000/mcL (must be obtained within 28 days prior to registration) * A total bilirubin =\< 1.5 x institutional limit normal (IULN) (must be obtained within 28 days prior to registration) * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 3.0 x IULN (or 5.0 x IULN if liver metastases are present) (must be obtained within 28 days prior to registration) * Serum creatinine =\< 1.5 x IULN OR calculated creatinine clearance \>= 40 mL/min (must have been obtained within 28 days prior to registration) * Patient must have urinary protein =\< 1+ on dipstick or routine urinalysis (UA) within 28 days prior to registration. If dipstick or routine analysis is \>= 2+, a 24 - hour urine collections for protein must demonstrate \< 1000 mg of protein in 24 hours * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients must not have known dihydropyrimidine dehydrogenase deficiency * Patients must be offered the opportunity to participate in specimen banking * Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines Exclusion Criteria: * Patients must not have received prior treatment with irinotecan, taxane, or ramucirumab for small bowel adenocarcinoma * Patients must not have had major surgery within 28 days prior to registration, or minor surgery within 7 days prior to registration, and must not be planned for elective major surgery to be performed during protocol treatment * Patients must not be currently enrolled in or have discontinued within the last 28 days a clinical trial involving an investigational product or non-approved use of a drug, or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study. Patients participating in surveys or observational studies are eligible to participate in this study * Patients must not be receiving chronic antiplatelet therapy, including dipyridamole or clopidogrel, or similar agents * Patient must not have a known bleeding diathesis * Patient must not have uncontrolled or poorly-controlled hypertension (\> 160 mmHg systolic or \> 100 mg HG diastolic for \> 4 weeks) despite standard medical management * Patient tumors must not have known deficient mismatch repair (dMMR) or microsatellite instability high (MSI-H) * Patients must not be pregnant or nursing and must have had a negative pregnancy test within 4 weeks of starting treatment. Women/men of reproductive potential must have agreed to use an effective contraceptive method. A woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months. In addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * Patients must not have an active infection requiring systemic therapy * Patient must not have liver dysfunctions manifested by either (1) Child-Pugh B (or worse) or (2) cirrhosis (any degree) and a history of hepatic encephalopathy or clinically meaningful ascites resulting from cirrhosis. Clinically meaningful ascites is defined as ascites from cirrhosis requiring diuretics or paracentesis * Patients must not have a history of deep vein thrombosis (DVT), pulmonary embolism (PE), or any other significant thromboembolism (venous port or catheter thrombosis or superficial venous thrombosis are not considered "significant") during the 90 days prior to registration * Patients must not have experienced any arterial thrombotic event (including but not limited to myocardial infarction, unstable angina, stable angina markedly limiting ordinary physical activity, cerebrovascular accident, or transient ischemic attack) within 120 days prior to registration * Patients must not have a prior history of gastrointestinal (GI) perforation/fistula or other risk factors for perforation within 120 days prior to registration * Patients must not have experienced any grade 3-4 GI bleeding within 90 days prior to registration * Patient must not have experienced any serious or non-healing wound, ulcer, or bone fracture within 28 days prior to registration