A Study of KX2-391 With Paclitaxel in Patients With Solid Tumors

Inclusion Criteria: Phase I Portion: \- Diagnosis of solid tumors on histopathological examination or cytological examination for which no standard of care is available or conventional treatment modalities have no therapeutic effect at the time of entering into the study Phase II Portion: * Diagnosis of advanced/metastatic/recurrent stomach cancer or breast cancer on histopathological examination or cytological examination for which no standard of care is available or conventional treatment modalities have no therapeutic effect at the time of entering into the study * Subjects with stomach cancer without prior taxane therapy * Subjects with breast cancer with prior taxane therapy * (Optional) Providing exploratory biomarker informed consent form to obtain archival tumor tissue and/or new tumor biopsy sample Common: 1. Based on clinical screening, ① If radiotherapy was given, at least 4 weeks should have passed from the last treatment date and the patient should have recovered from the toxicity (However, for limited regional radiotherapy, at least 2 weeks from the last treatment date) ② If hormonal therapy was given, at least 2 weeks should have passed from the last treatment date and the patient should have recovered from the toxicity. ③ If chemotherapy was given, at least 3 weeks should have passed from the last treatment date and the patient should have recovered from the toxicity (However, for nitrosourea or mitomycin, at least 6 weeks) 2. Aged ≥ 20 years 3. ECOG (Eastern Cooperative Oncology Group) ≤ 2 4. Life expectancy ≥ 12 weeks 5. Should meet the followings, ① Bone marrow function ANC (Absolute Neutrophil Count) ≥ 1.5 X 109/L, PLT (Platelet Count) ≥ 100 X 109/L, Hemoglobin ≥ 9.0 g/dl (In the case of hemoglobin of \< 9.0 g/dl, the patient can be enrolled if the value is reversed to ≥ 9.0 g/dl.) ② Kidney function Creatinine Clearance \> 50 ml/min or Serum Clearance ≤ 1.5 mg/dl ③ Liver function AST (Aspartate Aminotransferase)/ALT (Alanine Aminotransferase)/ALP (Alkaline Phosphatase) ≤ 3.0 X UNL and Total bilirubin ≤ 2.0 mg/dl (With bone metastasis, ALP ≤ 5.0 X UNL) 6. At least one measurable lesions with the length of the longest diameter of ≥ 10 mm on spiral CT or multidetector CT or ≥ 20 mm on conventional CT 7. Subjects who voluntarily consent to participate in this study and sign the written informed consent form Exclusion Criteria: 1. Uncontrolled central nervous system metastasis 2. Malignant ascites requiring surgical treatment 3. Subjects who have blood malignancies including leukemia; or who have received or will receive bone marrow transplantation 4. Severe concurrent diseases as follows, ① History of unstable angina, heart failure, atrial or ventricular arrhythmia requiring pharmacological treatment, or having received treatment for myocardial infarction within 6 months (however, may be included under the judgment of the investigator if medically controlled), heart failure of Class III or IV by New York Heart Association Classes, or left ventricular ejection fraction of \< 40% ② Receiving therapeutic dose administration of coumarin-type anticoagulants (however, up to 2 mg daily is permitted for line opening) ③ Uncontrolled diabetes (fasting plasma glucose \> 2.0 X UNL), severe hypertension, thyroid disorder and active infectious disease ④ Psychiatric or neurological history including dementia or epilepsy which may threaten the compliance with this protocol ⑤ A condition not allowing oral application of tablet formulation, and any clinically significant gastrointestinal abnormalities which may interfere with taking, passing or absorption of the study drug 5. Using disallowed concomitant medications (strong CYP3A4 (Cytochrome P450 3A4) inhibitors or inducers) (When a patient is using any of the disallowed concomitant medications below, wash-out of 1 week from the medication date is required) 6. Received other investigational product within 4 weeks prior to the administration of this study drug 7. Pregnant or breast-feeding women (however, women with 12 months of natural (spontaneous) amenorrhea or surgical bilateral oophorectomy (alone or with hysterectomy) at least 6 weeks ago, with appropriate clinical profile (e.g., appropriate age, history of vasomotor symptoms), will be considered women postmenopausal and of non-childbearing potential. In the case of oophorectomy alone, a woman will be considered to be of non-childbearing potential only if her reproductive condition is confirmed by follow-up hormone level assessment) 8. History of hypersensitivity to paclitaxel, compounds with similar chemical structure, or cremophor (polyoxyethylated castor oil) ingredient 9. Neuropathy of grade ≥ 3 based on clinical screening 10. Known history of hepatitis B or C and known history of HIV serum positive 11. Others unable to participate in the study under the judgment of the investigator