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,  Cancer of Cervix Tumors Male or female subjects age >18 years at the time of informed consent Histologically/cytologically confirmed locally advanced or metastatic solid tumors for which no curable therapy exists. In dose expansion part of this study, only patients with stage IV or recurrent/persistent cervical cancer will be enrolled. Confirmation of FGF/FGFR aberration is not required Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 Adequate marrow function as defined below: absolute neutrophil count ≥ 1.5 x 10 9/L platelets ≥ 100,000 x 10 9/L hemoglobin ≥ 9.0 g/dL Adequate liver function as evidenced by bilirubin <1.5 times the upper limit of normal (ULN); alanine aminotransferase (AL T) and aspartate aminotransferase (AST) <3 times the ULN Evidence of measurable or evaluable disease, as determined by v 1.1 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, for the duration of study participation, and for 90 days following completion of therapy. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. A female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following has not undergone a hysterectomy or bilateral oophorectomy, or has not been naturally postmenopausal for at least 12 consecutive months (Le., has had menses at any time in the preceding 12 consecutive months). Oral contraceptives (OC), injected or implanted hormonal methods are not allowed as the sole method of contraception because BGJ398 has not been characterized with respect to its potential to interfere with PK and/or the effectiveness of OCs It is preferred that archival tumor sample is available for molecular testing, if not available, a newly obtained tumor biopsy may be submitted instead (not mandatory)  For patients enrolled in dose escalation, any number of prior treatments allowed. For patients enrolled in dose expansion, no prior chemotherapy is allowed (previous single agent cisplatin concurrent with radiotherapy is accepted) No prior therapy with paclitaxel, BGJ398 or other FGFR targeting agents Preexisting> grade 2 peripheral neuropathy Patients with brain metastases are allowed provided that they are clinically stable for a period of 30 days prior to study entry and there is not a requirement for steroids or anti epileptics History of pancreatitis in last 6 months prior to enrollment History and/or current evidence of endocrine alterations of calcium/phosphate homeostasis, e.g., parathyroid disorders, history of parathyroidectomy, tumor lysis, tumoral calcinosis, or patients with other phosphate regulating abnormalities. Because hyperphosphatemia is a frequent occurrence with BGJ398 treatment, pretreatment and concurrent treatment with phosphate regulating agents is allowed Current evidence of corneal or retinal disorder/ keratopathy such as bullous/ band keratopathy, corneal abrasion, inflammation/ulceration, keratoconjunctivits, etc Since BGJ398 is a likely inhibitor of CYP3A4, patients who are currently receiving treatment with agents that are known sting inducers or inhibitors CYP3A4 are not allowed Treatment with any of the following anti-cancer therapies prior to the first dose of the of BGJ398 within the stated timeframes: intravenous chemotherapy within a period of 4 weeks ( 6 weeks for nitrosourea, mitomycin-C), biological therapy (e,g. antibodies) within a period of time that is ~ 5 t1/2 or less than 4 weeks, whichever is shorter, prior to starting study drug, any other investigational agents within a period of time that is < 5 tl/2 or 4 weeks (whichever is shortest) prior to starting study drug, wide field radiotherapy < 4 weeks or limited field radiation for palliation < 2 weeks prior to starting study drug Use of medications that increase serum levels of phosphorus and/or calcium