• Patients with histologically documented metastatic or locally advanced (not amenable to surgery) solid tumors whose disease has progressed following at least one line of standard therapy and/or no standard of treatment exists that has been shown to prolong survival.

‣ If anti-PD-1 or one of the 6 chemotherapy agents is standard-of-care, prior therapy with the agent would not be required.

• Patient must have tumor amenable to biopsy and be willing to undergo a tumor biopsy.

‣ Flash frozen tissue collected as part of another study or from a procedure performed due to medical necessity may be acceptable as the baseline sample if the samples were collected within 3 months prior to registration and the patient has not received any investigational or targeted treatment since that time.

⁃ A patient who cannot be safely biopsied may be considered for the study upon discussion with Principal Investigator.

• Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan.

• Patients with bone metastases or hypercalcemia on intravenous bisphosphonate treatment, denosumab, or similar agents are eligible to participate and may continue this treatment. Patients with prostate cancer may continue luteinizing hormone-releasing hormone (LHRH) agonists or antagonists.

• Age ≥ 18 years. Children are excluded from this study, but may be eligible for future pediatric trials.

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2.

• Absolute neutrophil count \>= 1,000/uL (mcL).

• Platelets \>= 100,000/uL (mcL).

• Total bilirubin \< 1.5 x institutional upper limit of normal.

‣ This will not apply to patients with confirmed Gilbert syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed only at the discretion of the principal investigator (PI), study chair or their designee.

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal, or up to 5 x upper limit of normal (ULN) if liver metastases are present.

• Calculated creatinine clearance \> 40 mL/min by the Cockcroft-Gault formula

• Any prior systemic therapy (including checkpoint inhibitors), or major surgery must have been completed \>= 3 weeks (\> 6 weeks for nitrosoureas or mitomycin C) or 5 half-lives of the agent, whichever is shorter, prior to enrollment on protocol, and toxicity from prior treatment must have recovered to eligibility levels. Radiation therapy must have been completed \>= 1 week prior to starting treatment. Radiofrequency ablation (RFA) of localized lesions should have been performed \>= 1 week prior to starting treatment. All radiation-related toxicity must have resolved to \< grade 2.

‣ Palliative radiotherapy is permitted between disease progression on Arm 1 and crossover to a combination therapy arm (Arms 2-7), provided there is a washout period of \>= 1 week and any toxicity from radiation has resolved to \< grade 2

⁃ Patients on any arm may receive palliative radiotherapy or loco-regional ablative therapy and remain on study, provided the radiation is not delivered to the target lesion and the patient does not have tumor progression by Response Evaluation Criteria in Solid Tumors (RECIST)

• Treatment with systemic immunostimulatory agents (including, but not limited to, interferon-alpha or interleukin-2) must have been completed at least 3 weeks before the first dose of durvalumab.

• Body weight \> 30 kg.

• Human immunodeficiency virus (HIV)-infected (HIV1/2 antibody-positive) patients may participate if they meet all the following eligibility requirements:

‣ They must be on an anti-retroviral regimen with evidence of at least two undetectable viral loads within the past 6 months on this same regimen; the most recent undetectable viral load must be within the past 12 weeks.

⁃ They must have a CD4 count \>= 250 cells/uL over the past 6 months on this same anti-retroviral regimen and must not have had a CD4 count \< 200 cells/uL over the past 2 years, unless it was deemed related to chemotherapy-induced bone marrow suppression.

∙ For patients who have received chemotherapy in the past 6 months, a CD4 count \< 250 cells/uL during chemotherapy is permitted as long as viral loads were undetectable during this same chemotherapy.

⁃ They must have an undetectable viral load and a CD4 count \>= 250 cells/uL within 28 days of enrollment.

⁃ They must not be currently receiving prophylactic therapy for an opportunistic infection and must not have had an opportunistic infection within the past 6 months.

⁃ Monitoring for HIV-infected patients should include:

∙ Viral load and CD4 count every 8-10 weeks.

• The effects of targeted agents on the developing human fetus are unknown. The cytotoxic agents chosen for combination with durvalumab adversely affect human fertility and gestation. For these reasons, women of childbearing potential and men must agree to use highly effective contraception prior to study entry for the duration of study participation and for 6 months following the last dose of a study drug.

• Because there may be a risk for adverse events in nursing infants secondary to treatment of the mother with these agents, breastfeeding should be discontinued while the patient is on this trial and for 6 months following the last dose of study drug.

• Patients should be willing not to donate blood while participating in this study or for at least 90 days following the last dose of study drug.

• Left ventricular ejection fraction greater than 50% or the institutional lower limit of normal by echocardiography (ECHO) at entry (patients enrolling on Arm 3 only).

• Ability to understand and the willingness to sign a written informed consent document.