Testing the Addition of an Anticancer Drug, Olaparib, to the Usual Chemotherapy (Temozolomide) for Advanced Neuroendocrine Cancer

Inclusion Criteria:

* Documentation of disease

  * Histologic documentation: Histologically-proven advanced (metastatic or unresectable primary) pheochromocytoma or paraganglioma
  * Stage: Advanced (metastatic or unresectable primary) disease
  * Tumor site: Histologically-proven pheochromocytoma or paraganglioma
  * Radiographic evaluation: Radiographic evidence of disease progression by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 in the 12 months prior to registration
* Measurable disease

  * Lesions must be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 1 cm with CT or MRI (or \>= 1.5 cm for lymph nodes). Non-measurable disease includes disease smaller than these dimensions or lesions considered truly non-measurable including: leptomeningeal disease, ascites, pleural or pericardial effusion, lymphangitic involvement of skin or lung
* Prior treatment with other somatostatin analog, chemotherapy, radiotherapy (including peptide radionuclide receptor therapy \[PRRT\]), or surgery must be completed \>= 28 days prior to registration. Patients must have recovered from any effects of any major surgery prior to registration
* Prior treatment with radiolabeled metaiodobenzylguanidine (MIBG) must be completed \>= 12 weeks prior to registration and lifetime cumulative 131I-MIBG dose must be \< 1000 MBq kg\^-1 (36 mCi kg\^-1)
* Prior treatment with antibiotics must be completed \>= 7 days prior to registration
* No prior treatment with temozolomide, dacarbazine, or a poly ADP ribose polymerase (PARP) inhibitor
* No prior allogeneic bone marrow transplant or double umbilical cord blood transplantation (dUCBT)
* Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic, and teratogenic effects. Therefore, for women of childbearing potential only, a negative pregnancy test done =\< 7 days prior to registration is required
* Contraception

  * Therapy utilized in this trial is associated with medium/high fetal risk
  * Women of childbearing potential and their partners, who are sexually active, must agree to use two highly effective forms of contraception in combination. This should be started from the time of registration and continue throughout the period of taking study treatment and for at least 1 month after last dose of study drug(s), or they must totally/truly abstain from any form of sexual intercourse
  * Male patients must use a condom during treatment and for 3 months after the last dose of study drug(s) when having sexual intercourse with a pregnant woman or with a woman of childbearing potential. Female partners of male patients should also use a highly effective form of contraception if they are of childbearing potential. Male patients should not donate sperm throughout the period of taking study drug(s) and for 3 months following the last dose of study drug(s)
* Age \>= 12 years
* Eastern Cooperative Oncology Group (ECOG) Patients ≥ 18 years of age: Performance status: 0-2

  * Patients \< 16 years of age: Lansky ≥ 50%
  * Patients 16 to \< 18 years of age: Karnofsky ≥ 50%
  * Patients ≥ 18 years of age: ECOG performance status ≤ 2
* Absolute neutrophil count \>= 1,500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Hemoglobin \>= 10 mg/dL if prior radionuclide therapy Hemoglobin \>= 8 mg/dL if no prior radionuclide therapy

  * In the absence of transfusion within the previous 24 hours. Radionuclide therapy includes PRRT or MIBG
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)

  * Except in the case of Gilbert's syndrome, then total bilirubin must be =\< 3.0 x ULN
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3.0 x ULN
* Creatinine \< 1.5 x ULN OR calculated (calc.) creatinine clearance \> 50 mL/min

  * Calculated by Cockcroft-Gault equation
  * By Cockcroft-Gault equation. Alternatively, for patients \< 18 years of age, maximum serum creatinine ≤ the below age-sex-specific norms:

    * Age 12 years: Male 1.2; female 1.2
    * Age 13 to \< 16 years: Male 1.5; female 1.4
    * Age 16 to \< 18 years: Male 1.7; female 1.4
* No indication of uncontrolled, potentially reversible cardiac condition(s) as determined by investigator (e.g., unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, Fridericia's formula-corrected QT interval \[QTcF\] prolongation \> 500 msec, electrolyte disturbances, etc.) and no known congenital long QT syndrome
* No extensive bilateral lung disease or pneumonitis
* No abnormal organ or bone marrow function =\< 28 days prior to registration
* Patients with human immunodeficiency virus (HIV) positivity are allowed if CD4 count \> 250 cells/uL and they have an undetectable HIV viral load within 6 months of registration
* No active infection
* No history of myelodysplastic syndrome (MDS) (or any dysplastic leukocyte morphology suggestive of MDS) or acute myeloid leukemia
* No known gastrointestinal condition(s) that might predispose for drug intolerability or poor drug absorption
* No known medical condition causing an inability to swallow oral formulations of agents
* No history of allergic reaction attributed to compounds of similar chemical or biologic composition to PARP inhibitors
* Concurrent use of combination antiretroviral therapy (ART) is not permitted
* Chronic concomitant treatment with strong or moderate CYP3A4 inducers or inhibitors is not allowed. Patients must discontinue the agent(s) \>= 21 days prior to registration; enzalutamide and/or phenobarbital must be discontinued \>= 5 weeks prior to registration