NET RETREAT: A Phase II Study of 177 Lutetium-DOTATATE Retreatment vs. Everolimus or Sunitinib or Cabozantinib in Metastatic/Unresectable Gastroenteropancreatic Neuroendocrine Tumours

Inclusion Criteria: * Patients must be at least \>= 18 years of age * Metastatic, histologically confirmed grade 1 or 2 well-differentiated gastroenteropancreatic neuroendocrine tumours, including NETs of unknown primary thought to be of gastroenterogancreatic origin, with positive Gallium-68 DOTATATE scan, Copper-64 DOTATATE scan or octreotide scan within the last 12 months is recommended but within the last 36 months is allowed. Lesions on Gallium-68 or Copper-64 DOTATATE scan or octreotide scan will be considered positive if the maximum standardized uptake value (SUVmax) of target lesion is \> SUV mean of normal liver parenchyma * 7th Edition of the TNM Classification of Malignant Tumours * Have received 3 or 4 cycles of PRRT using 177Lu-DOTATATE or a cumulative exposure of 22,200 MBq (600mCi) or 29,600 MBq (800 mCi) within +/- 10% variation within a 52-week period. No previous targeted alpha therapy is permitted * Have had radiological progression per RECIST 1.1 after prior PRRT treatment and no sooner than 12 months from last scan performed post completion of initial PRRT where either stable disease, partial response, or complete response has been maintained throughout. Patients may have received previous systemic anti-cancer therapy subsequently, as long as they had benefited from initial PRRT for at least 12 months and have had confirmed progression per RECIST 1.1 on the intervening systemic anti-cancer therapy. Somatostatin analogues (SSA) administered for functional control are not considered an intervening systemic anti-cancer therapy. If intervening systemic anti-cancer therapy included a vascular endothelial growth factor (VEGF)-inhibitor, sunitinib can not be selected as standard of care on Arm 2. If intervening systemic anti-cancer therapy included an mammalian target of rapamycin (mTOR)-inhibitor, then everolimus can not be selected as the standard of care on Arm 2. If the intervening therapy is an alkylating agent, exposure of alkylating agent cannot exceed 12 months. The 12-month limit will also be applied to pre PRRT alkylator use as well * Patients may have received previous ablative therapy or bland embolization as liver directed therapy however this must not have been received within 12 weeks from randomization date. Previous chemo and radio embolization are not permitted. Any lesion treated with an ablative technique as well as lesions in the lobe(s) of the liver treated with embolization shall not be included in target lesion assessment unless they have since progressed * No ongoing toxicity from prior PRRT that is grade 3 or higher according to Common Terminology Criteria for Adverse Events (CTCAE) 5.0 * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Hemoglobin \>= 80 g/L (\>= 8.0 g/dL) (measured within 28 days prior to enrollment) * Absolute neutrophil count \>= 1.0 x 10\^9/L (\>= 1000/mm\^3) (measured within 28 days prior to enrollment) * Platelets \>= 80 x 10\^9/L (\>= 80 x 10\^3/mm\^3) (measured within 28 days prior to enrollment) * Total bilirubin \< 1.5 x upper limit of normal (ULN) (upper limit of normal) (measured within 28 days prior to enrollment) * If confirmed Gilbert's, eligible providing =\< 3.0 x ULN * Creatinine clearance \> 50 mL/min (measured within 28 days prior to enrollment) * Creatinine clearance to be measured directly by 24 hour urine sampling or as calculated by Cockcroft and Gault equation * Prior or current use of somatostatin analogues is allowed for carcinoid syndrome control or in PRRT re-treatment patient population (Arm 1). Patients randomized to Arm 2 and receiving everolimus or sunitinib (pancreatic NET patients only) or cabozantinib (US patients only) will not be allowed to continue somatostatin analogues unless they have functional syndrome * Patient consent must be appropriately obtained in accordance with applicable local and regulatory requirements. Each patient must sign a consent form prior to enrollment in the trial to document their willingness to participate * Males and females of reproductive potential must have agreed to use a highly effective contraceptive method during protocol treatment and for 7 months after the last dose of protocol treatment for females and 4 months after the last dose of protocol treatment for males. A woman is considered to be of "childbearing 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, or vasectomy/vasectomized partner. 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. Men should avoid fathering a child for 4 months after the last dose of 177Lu-DOTATATE * Women of childbearing potential will have a pregnancy test to determine eligibility as part of the Pre-Study Evaluation; this may include an ultrasound to rule-out pregnancy if a false-positive is suspected. For example, when beta-human chorionic gonadotropin is high and partner is vasectomized, it may be associated with tumour production of human chorionic gonadotropin (hCG), as seen with some cancers. Patient will be considered eligible if an ultrasound is negative for pregnancy * Patients must be accessible for treatment, response assessment, and follow up. Patients enrolled on this trial must be treated and followed at the participating center. Investigators must assure themselves the patients enrolled on this trial will be available for complete documentation of the treatment, adverse events, and follow-up * Patients must agree to return to their primary care facility for any adverse events which may occur through the course of the trial * Patient must have access to everolimus or sunitinib (pancreatic NET patients only) or cabozantinib (US patients only). In the event that site/investigator is unable to provide access to the drug, patient will not be eligible for this trial * Human immunodeficiency virus (HIV) infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * 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 Exclusion Criteria: * Major surgical procedures within 6 weeks from randomization date * Known brain metastases, unless these metastases have been treated, stabilized and off steroids for at least 4 weeks prior to enrollment in the study. Patients with a history of brain metastases must have a head CT and/or MRI with contrast to document stable disease prior to enrollment in the study * Uncontrolled congestive heart failure no worse than New York Heart Association Class (NYHA) IIB * Inability to swallow oral medications or gastrointestinal disease limiting absorption of oral agents * Patients with any other significant medical or surgical condition, currently uncontrolled by treatment, which may interfere with completion of the study * Pregnant women are excluded from this study because 177Lu-DOTATATE is a peptide receptor radionuclide therapy with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with 177Lu-DOTATATE, breastfeeding should be discontinued if the mother is treated with everolimus or sunitinib or cabozantinib (US patients only) and for 2.5 months following the last treatment with 177Lu-DOTATATE