Patient description: The patient is a 37-year-old woman who came to the clinic for a routine Pap smear. The test revealed stage 1B of cervical cancer. The patient tested positive for HPV 16. She has three sexual partners and four children. She underwent tubal ligation. She smokes 30 packs/year and drinks alcohol frequently. She is otherwise healthy. She was offered a radical hysterectomy.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  BRAF V600E Mutation Present BRAF V600K Mutation Present Metastatic Malignant Solid Neoplasm Metastatic Melanoma Stage III Cutaneous Melanoma AJCC v7 Stage IIIA Cutaneous Melanoma AJCC v7 Stage IIIB Cutaneous Melanoma AJCC v7 Stage IIIC Cutaneous Melanoma AJCC v7 Stage IV Cutaneous Melanoma AJCC v6 and v7 Unresectable Solid Neoplasm Patients must have histologically confirmed, BRAF-mutant (V600E/K) solid tumor (molecularly confirmed using Cobas assay or a comparable Food and Drug Administration [FDA]-approved assay) that is metastatic or unresectable, have received and tolerated prior BRAF or BRAF and MEK inhibitor (BRAF targeted) therapy at full dose or not previously received BRAF targeted therapy, and for which standard curative measures do not exist or are no longer effective If test at Clinical Laboratory Improvement Act (CLIA)-certified laboratory (lab) used a non-FDA approved method, information about the assay must be provided; (FDA approved tests for BRAF V600 mutations in melanoma THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test) 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 for non-nodal lesions and short axis for nodal lesions) as >= 20 mm with conventional techniques or as >= 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam Prior therapy is allowed; patients may have received any number of prior lines of therapy, including treatment with a BRAF and/or MEK inhibitor All prior anti-cancer treatment-related toxicities must be less than or equal to grade 1 according to the Common Terminology 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) Eastern Cooperative Oncology Group (ECOG) performance status =< 1 (Karnofsky >= 70%) Life expectancy of greater than 3 months Leukocytes >= 3,000/mcL Absolute neutrophil count >= 1,200/mcL Hemoglobin >= 9 g/dl (patients may be transfused to this level)  Patients who received prior systemic anti-cancer therapy (chemotherapy with delayed toxicity, extensive radiation therapy, immunotherapy, biologic therapy, or vaccine therapy) within the last 3 weeks prior to day 1 of cycle 1; patients are permitted to be on dabrafenib and trametinib standard of care at start of therapy without wash-out period prior to day 1 of cycle 1; dosing will change to protocol determined dose levels on day 1 of cycle 1 Patients must not have received prior HSP90 inhibitor therapy Patients who are receiving any other investigational agents; patients who have taken an investigational drug within 28 days or 5 half-lives (minimum 14 days), whichever is shorter, prior to randomization Patients with history of activating RAS mutation positive tumors regardless of interval from current study; however, patients may have concurrent BRAFV600 and RAS mutations in the tumor to be treated with protocol therapy Patients must have no clinical evidence of leptomeningeal or brain metastasis causing spinal cord compression that are symptomatic or untreated or not stable for >= 4 weeks (must be documented by imaging) or requiring corticosteroids; subjects on a stable dose of corticosteroids > 1 month or who have been off of corticosteroids for at least 2 weeks can be enrolled with approval of the Cancer Therapy Evaluation Program (CTEP) medical monitor; subjects must also be off of enzyme-inducing anticonvulsants for > 4 weeks History of known immediate or delayed hypersensitivity reactions attributed to compounds of similar chemical or biologic composition to AT13387, dabrafenib, or trametinib, or excipients or to dimethyl sulfoxide (DMSO) Uncontrolled intercurrent illness including, but not limited to, ongoing or active serious infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, uncontrolled diabetes, or psychiatric illness/social situations that would limit compliance with study requirements Pregnant women are excluded from this study; breastfeeding should be discontinued prior to the mother being treated with the study drugs Patients known to be human immunodeficiency virus (HIV)-positive patients and on combination antiretroviral therapy are ineligible History of another malignancy other than the study indication under this trial within 5 years of study enrollment; does not apply to subjects who underwent successful definitive resection of basal or squamous cell carcinoma of the skin, superficial bladder cancer, in situ cervical cancer, in situ breast cancer, or other in situ cancers