Rapid Analysis and Response Evaluation of Combination Anti-Neoplastic Agents in Rare Tumors (RARE CANCER) Trial: RARE 1 Nilotinib and Paclitaxel

* INCLUSION CRITERIA: * Patients must have histologically confirmed rare solid tumors that have progressed on standard therapy known to prolong survival or for which no standard treatment options exist. The list of eligible rare tumors can be found below\*\*. With Amendment G (v 6-17-24), eligibility will be limited to patients with adult granulosa cell ovarian cancer, clear cell ovarian cancer, anal cancer, or Ewing sarcoma.Patients must have measurable and evaluable disease. * Age \>= 18 years. * ECOG performance status \<= 2. * Patients must have normal organ and marrow function as defined below: * Absolute neutrophil count \>=1,500/mcL * Platelets \>=100,000/mcL * Total bilirubin \<=1.5 X institutional ULN * AST(SGOT)/ALT(SGPT) \<=3 X institutional upper limit of normal; \<= 5.0 x ULN in patients with liver metastases * creatinine \<=1.5 X institutional ULN OR * creatinine clearance \>=60 mL/min/1.73 m\^2 for patients with creatinine levels \>1.5 mg/dL * Nilotinib and paclitaxel have both been assigned to pregnancy category D by the FDA. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and for at least 3 months after dosing with study drugs ceases. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 3 months after completion of study drug administration. * Patients must have completed radiation therapy or major surgery \>= 3 weeks, or biologic therapy or chemotherapy \>= 5 half-lives or 3 weeks, whichever is shorter (6 weeks for nitrosoureas and mitomycin C) prior to entering the study. Patients must be \>= 2 weeks since any prior administration of a study drug in a Phase 0 or equivalent study and be \>= 1 week from palliative radiation therapy (patients on study may be eligible for palliative radiotherapy to non-targeted lesions after 2 cycles of therapy at the PI s discretion). Patients must have recovered to eligibility levels from prior toxicity or adverse events. Treatment with bisphosphonates is permitted. * Biopsies are optional on this study. In lieu of baseline biopsies, patients are encouraged to submit at registration archival tumor biopsy tissue from a previous research study or medical care providing it meets the minimum collection and preservations requirements outlined for the submission of archival tissue are: * Tissue must have been collected within 3 months prior to registration. * Patient must not have received any intervening therapy for their cancer since the collection of the tumor sample. * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. For these patients, an HIV viral load test must be completed within 28 days prior to enrollment. * Rare Tumor Eligibility List 1. Epithelial tumors of nasal cavity, sinuses, nasopharynx 2. Epithelial tumors of major salivary glands 3. Salivary gland type tumors of head and neck, lip, esophagus, stomach, trachea and lung, breast and other location 4. Undifferentiated carcinoma of gastrointestinal (GI) tract 5. Adenocarcinoma with variants of small intestine 6. Squamous cell carcinoma with variants of GI tract (stomach small intestine, colon, rectum, pancreas) 7. Fibromixoma and low-grade mucinous adenocarcinoma (pseudomixoma peritonei) of the appendix and ovary 8. Rare Pancreatic tumors including acinar cell carcinoma, mucinous cystadenocarcinoma or serous cystadenocarcinoma 9. Intrahepatic cholangiocarcinoma 10. Extrahepatic cholangiocarcinoma and bile duct tumors 11. Sarcomatoid carcinoma of lung 12. Bronchoalveolar carcinoma lung (a.k.a. adenocarcinoma in situ, minimally invasive adenocarcinoma, lepidic predominant adenocarcinoma, or invasive mucinous adenocarcinoma) 13. Non-epithelial tumors of the ovary 14. Trophoblastic tumor 15. Transitional cell carcinoma other than that of the renal, pelvis, ureter, or bladder 16. Cell tumor of the testes and extragonadal germ tumors 17. Epithelial tumors of penis - squamous adenocarcinoma cell carcinoma with variants of penis 18. Squamous cell carcinoma variants of the genitourinary (GU) system 19. Spindle cell carcinoma of kidney, pelvis, ureter 20. Adenocarcinoma with variants of GU system (excluding prostate cancer) 21. Odontogenic malignant tumors 22. Pancreatic neuroendocrine tumor (PNET) 23. Neuroendocrine carcinoma including carcinoid of the lung 24. Pheochromocytoma, malignant 25. Paraganglioma 26. Carcinomas of pituitary gland, thyroid gland parathyroid gland and adrenal cortex 27. Desmoid tumors 28. Peripheral nerve sheath tumors and NF1-related tumors 29. Malignant giant cell tumors 30. Chordoma 31. Adrenal cortical tumors 32. Tumor of unknown primary (Cancer of Unknown Primary; CuP) 33. Not Otherwise Categorized (NOC) Rare Tumors 34. Adenoid cystic carcinoma 35. Vulvar cancer 36. MetaPLASTIC carcinoma (of the breast) 37. Gastrointestinal stromal tumor (GIST) 38. Perivascular epithelioid cell tumor (PEComa) 39. Apocrine tumors/Extramammary Paget s Disease 40. Peritoneal mesothelioma 41. Basal cell carcinoma 42. Clear cell cervical cancer 43. Esthenioneuroblastoma 44. Endometrial carcinosarcoma (malignant mixed Mullerian tumors) 45. Clear cell endometrial cancer 46. Clear cell ovarian cancer 47. Gestational trophoblastic disease (GTD) 48. Gallbladder cancer 49. Small cell carcinoma of the ovary, hypercalcemic type 50. Angiosarcoma 51. High-grade neuroendocrine carcinoma 52. Treatment-emergent small-cell neuroendocrine prostate cancer (t-SCNC) 53. Anal cancer 54. Lymphoma 55. Merkel cell carcinoma 56. Pleural Mesothelioma 57. Sarcoma (bone \& soft tissue) 58. Thymic Carcinoma 59. Uterine Leiomyosarcoma 60. Papillary RCC EXCLUSION CRITERIA: * QTcF interval of \>=450 msec at study entry; congenital long QT syndrome * Sensory/motor neuropathy \>= Grade 2 * Patients who are receiving any other investigational agents. * Patients with known primary central nervous system (CNS) malignancy or symptomatic CNS metastases are excluded, with the following exceptions: * Patients with asymptomatic untreated CNS disease may be enrolled, provided all of the following criteria are met: * Evaluable or measurable disease outside the CNS * No metastases to brain stem, midbrain, pons, medulla, or cerebellum * No history of intracranial hemorrhage or spinal cord hemorrhage * No ongoing requirement for dexamethasone for CNS disease; patients on a stable dose of anticonvulsants are permitted. * No neurosurgical resection or brain biopsy within 28 days prior to Cycle 1, Day 1 * Patients with asymptomatic treated CNS metastases may be enrolled, provided all the criteria listed above are met as well as the following: * Radiographic demonstration of improvement upon the completion of CNS-directed therapy and no evidence of interim progression between the completion of CNS-directed therapy and radiographic screening for the current study * No stereotactic radiation or whole-brain radiation within 28 days prior to Cycle 1, Day 1 * Screening CNS radiographic study \>=4 weeks from completion of radiotherapy and \>=2 weeks from discontinuation of corticosteroids * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study drugs. * Uncontrolled intercurrent illness including, but not limited to, serious untreated infection, symptomatic respiratory failure/congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study because nilotinib and paclitaxel have been assigned to pregnancy category D by the FDA. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with the study drugs, breastfeeding should be discontinued prior to the first dose of study drug and women should refrain from nursing throughout the treatment period and for 3 months following the last dose of study drug.