Patients must not currently have a > grade 1 symptomatic neuropathy-sensory (National Cancer Institute [NCI] Common Terminology Criteria for Adverse Events [CTCAE] version 4.0)Xx_NEWLINE_xXAny unresolved chronic toxicity with CTCAE grade >= 2, from previous anti-NF1 therapy, except for alopeciaXx_NEWLINE_xXUnresolved toxicity of National Cancer Institute Common Terminology Criteria for Adverse Events, version 4.0 (NCI CTCAE v4.0) grade 2 or higher from previous anti-cancer therapy, except alopecia; in specific cases, will be allowed with permission from the principal investigatorXx_NEWLINE_xXUnresolved toxicity of National Cancer Institute Common Terminology Criteria for Adverse Events, version 5.0 (NCI CTCAE v. 5.0) grade 2 or higher from previous anti-cancer therapy, except alopecia, at the time of randomizationXx_NEWLINE_xXAll prior anti-cancer treatment-related toxicities must be less than or equal to grade 1 according to the Common Terminology Criteria for Adverse Events version 5 (CTCAE version 5.0; National Cancer Institute [NCI], 2017) at the time of enrollment; a notable exception are endocrinopathies caused by immune checkpoint inhibitors that are appropriately treated with medical management (e.g. hormone replacement therapy, anti-diabetic agents)Xx_NEWLINE_xXPatients should have resolution of any toxic effects of prior therapy (except alopecia) to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 5.0, grade 1Xx_NEWLINE_xXUnresolved toxicity of National Cancer Institute Common Terminology Criteria for Adverse Events, version 4.0 (NCI CTCAE v 4.0) grade 2 or higher from previous anti-cancer therapy, except alopeciaXx_NEWLINE_xXPatients must not have any unresolved toxicity greater than National Cancer Institute (NCI)-CTCAE version (v) 4.0 grade 1 from previous anti-cancer therapy except alopecia within 7 days prior to registrationXx_NEWLINE_xXNo ongoing cardiac dysrhythmias of grade >= 2 National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 4.0, uncontrolled atrial fibrillation (any grade), or corrected QT (QTc) interval > 470 msecXx_NEWLINE_xXUnresolved toxicities from prior anti-cancer therapy, defined as having not resolved to Common Terminology Criteria for Adverse Event (CTCAE, version 4), grade =< 1, or to the levels dictated in the inclusion/exclusion criteria with the exception of alopeciaXx_NEWLINE_xXUnresolved toxicity of National Cancer Institute Common Terminology Criteria for Adverse Events, version 4.0 (NCI CTCAE v4.0) grade 2 or higher from previous anti-cancer therapy, except alopecia, at the time of randomizationXx_NEWLINE_xXPatients should have resolution of any toxic effects of prior therapy (except alopecia) to NCI CTCAE, version 4.0, grade 1 or lessXx_NEWLINE_xXPatients should have resolution of any toxic effects of prior therapy (except fatigue and alopecia) to NCI CTCAE, version 4.0, grade 1 or less, including immune toxicityXx_NEWLINE_xXDiarrhea >= grade 1, based on the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) categorization within 14 days of registrationXx_NEWLINE_xXHave any unresolved chronic toxicity with CTC AE grade >= 2, from previous anti-NF1 therapy, except for alopeciaXx_NEWLINE_xXToxicities of prior therapy (excepting alopecia) should be resolved to less than or equal to grade 1 as per National Cancer Institute-Common Terminology Criteria for Adverse Events (NCI-CTCAE); patients with long-standing stable grade 2 neuropathy may be considered after discussion with the overall principal investigator (PI), but may not receive carboplatin and paclitaxel as the reference regimen, if randomized to that armXx_NEWLINE_xXToxicities of prior therapy (except alopecia) should be resolved to =< grade 1 as per National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0; patients with long-standing stable grade 2 neuropathy may be considered after discussion with the study principal investigator (PI)Xx_NEWLINE_xXPatients should have resolution of any toxic effects of prior therapy (except alopecia) to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 4.0, grade 1 or lessXx_NEWLINE_xXUnresolved toxicity higher than CTCAE grade 1 attributed to any prior therapy/procedure, excluding alopeciaXx_NEWLINE_xXHave any unresolved chronic toxicity with CTCAE grade >= 2, from previous anti-NF1 therapy, except for alopeciaXx_NEWLINE_xXPatients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met: minimum of 12 weeks from the first dose of anti-CTLA-4 and > 6 weeks from the last dose, and no history of severe immune-related adverse effects from anti-CTLA-4 (National Cancer Institute [NCI] Common Terminology Criteria for Adverse Events [CTCAE] grade 3 and 4)Xx_NEWLINE_xXPatients who have received prior treatment with anti-CTLA-4 antibody may be enrolled, provided the following requirements are met:* > 6 weeks from the last dose* No history of severe immune-related adverse effects from anti-CTLA-4 antibody (National Cancer Institute [NCI] Common Terminology Criteria for Adverse Events [CTCAE] grade 3 and 4)Xx_NEWLINE_xXAny unresolved toxicity National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade >= 2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria* Patients with grade >= 2 neuropathy will be evaluated on a case-by-case basis after consultation with the study physician; patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab or tremelimumab may be included only after consultation with the study physicianXx_NEWLINE_xXToxicities of prior therapy (except alopecia) should be resolved to =< grade 1 as per National Cancer Institute-Common Terminology Criteria for Adverse Events (NCI-CTCAE) v5.0; patients with long-standing stable grade 2 neuropathy or others (e.g., adrenal insufficiency or hypothyroidism on stable doses of replacement therapy) may be allowed after discussion with the study principal investigator (PI)Xx_NEWLINE_xX