Avatar-Directed Chemotherapy in Treating Patients With Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Histologic confirmation of ovarian, primary peritoneal or fallopian tube cancer of any subtype * Prior consent to have tumors used for unspecified future research * Ability to provide written informed consent * Willing to agree to periodic contact with a member of the study team during the period that the cancer has not recurred and/or has not become platinum resistant * Willing to agree that the local medical oncologist may be informed that patient has agreed to participate in the study * Platinum resistant or refractory ovarian, primary peritoneal or fallopian tube cancer of any subtype; Note: platinum-sensitive disease is allowed in cases where there is a contraindication to platinum-based therapy (i.e., allergy to platinum); this must be reviewed and approved by the Principal Investigator * Successful Avatar engraftment with successful expansion and treatment outcome of Avatar therapy * Eastern Cooperative Oncology Group (ECOG) performance status (ECOG performance status \[PS\]) of 0, 1 or 2 * Measurable disease or non-measurable disease; for patients with non-measureable disease, they must also have a cancer antigen (CA)-125 measurement of \> 35 U/mL or 2 X their documented nadir on 2 separate measurements 1 week apart * The following laboratory values obtained =\< 21 days prior to registration; complete blood count (CBC), sodium, potassium, aspartate aminotransferase (AST), bilirubin and creatinine are to be obtained pre-study; Note: treatment initiation and dosing modification should be performed at the individual investigators discretion and be consistent with the product label and their medical practice * Negative urine or serum pregnancy test performed =\< 7 days prior to registration, for women of child bearing potential only * Willing to return to enrolling institution for follow-up or have a local physician willing to submit response and outcome data; Note: any and all therapy, potentially in its entirety, may be conducted outside of the Mayo Clinic Exclusion Criteria: * Any of the following: * Pregnant women * Nursing women * Prior treatment with Doxil, topotecan, Gemzar or Taxol chemotherapy for platinum-resistant cancer; Note: Allowed prior therapy with Doxil or Gemzar if given for platinum sensitive disease in combination with a platinum drug AND the Avatar data indicates a drug other than Doxil or Gemzar would be effective; Note: Allowed prior therapies for patients following confirmation of platinum-resistant cancer include: * Therapeutic antibodies, such as bevacizumab * Small molecule kinase inhibitors, such as pazopanib * Vaccines and immunotherapy All of these exceptions should be confirmed with the Principal Investigator (PI) prior to registration * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy; Note: patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial * Uncontrolled intercurrent illness judged by the treating investigator to preclude treatment with chemotherapy * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Other active malignancy =\< 3 years prior to registration; EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; Note: if there is a history of prior malignancy, they must not be receiving treatment for their cancer