• To quantify the occurrence of adverse events (AEs) reported in all subjects who received study drug [ Time Frame: From enrollment up to 30 days after last dose ]
  Incidence of untoward medical occurrences (adverse event = AE) in a participant who received study drug. Adverse events will be evaluated by dosing cohort and recorded according to NCI CTCAEv5 Common Toxicity Criteria.
• To determine the occurrence of treatment-emergent adverse events (TEAs) [ Time Frame: From first dose up to 30 days after last dose ]
  Incidence of untoward medical occurrences (adverse event = AE) attributed to study drug in a participant who received study drug. Adverse events will be evaluated and recorded by dosing cohort according to NCI CTCAEv5 Common Toxicity Criteria.
• To determine the occurrence of treatment-related adverse events meeting the criteria for dose limiting toxicities (DLTs) [ Time Frame: From first dose up to 28 days ]
  Incidence of the DLT population will consist all subjects who received the required amount of study drug during the DLT observation period of 28 days (21 days of daily dosing, 7 days of no dosing) of study treatment . Treatment-related AE is any untoward medical occurrence attributed to study drug in a participant that who received study drug. Treatment-related AE is any untoward medical occurrence attributed to study drug in a participant who received study drug. DLTs are adverse events meeting the protocol-specified criteria, evaluated and recorded according to NCI CTCAEv5 Common Toxicity Criteria will use medical terminology based on the Medical Dictionary for Regulatory Activities Terminology (MedDRA).

• To quantify the area under the serum concentration versus time curve (AUC) of FCN-437c after administration as a single agent [ Time Frame: 2 months ]
  Quantify the dose-dependent area under the serum concentration versus time curve (AUC) for FCN-437c following single dosing FCN-437c
• To quantify the last time point with a quantifiable concentration (AUClast) of FCN-437c after administration as a single agent [ Time Frame: 2 months ]
  Determine the dose-dependent plasma concentrations of FCN-437c from the time of dosing to the last time point with a quantifiable concentration (AUClast) of FCN-437-c following single doses of FCN-437c as a single agent.
• To quantify the plasma concentrations at the end of a dosing interval (Ctau) of FCN-437c after administration as a single agent [ Time Frame: 2 months ]
  Determine the dose-dependent serum concentrations (Cmax) of FCN-437c as as a single agent at the end of a dosing interval (Ctau), where tau is 24 hours
• To quantify the lowest plasma concentration at the end of a dosing interval (Ctrough) [ Time Frame: 2 months ]
  Determine the dose-dependent lowest plasma concentrations (Ctrough) of FCN-437c as a single agent at the end of a dosing interval
• To measure the time to reach the highest plasma concentrations (Tmax) of FCN-437c after single agent administration [ Time Frame: 2 months ]
  Determine the dose-dependent time (Tmax) to reach the highest plasma concentrations of FCN-437c by direct inspection of the plasma concentration time curves of FCN-437c following single agent doses of FCN-437c
• To quantify the terminal half-life (T1/2) of FCN-437c after administration as a single agent [ Time Frame: 2 months ]
  Determine the dose-dependent terminal plasma half-life of FCN-437 (T 1/2) as single agent
• To quantify the plasma clearance (CL/f) of FCN-437c after administration as a single agent [ Time Frame: 2 months ]
  Determine the dose-dependent apparent total plasma clearance (CL/f) of FCN-437c after administration as a single agent
• To evaluate the volume of distribution (Vf) of FCN-437c after administration as a single agent [ Time Frame: 2 months ]
  Determine the apparent steady-state volume of distribution (Vf) during terminal phase after administration of FCN-437c as single agent
• To determine the best overall response rate (ORR) by Response Criteria in Solid Tumors (RECIST) v1.1 in subjects with advanced solid tumors [ Time Frame: Baseline up to approximately 1 year ]
  To evaluate the proportion of patients with an objective response (SD, PR, CR) as defined by RECIST 1.1.

• To correlate the degree of tumor-specific CDK4/6 inhibition to the dose level of FCN-437c [ Time Frame: Baseline up to approximately 1 year ]
  Determine the association between plasma levels of FCN-437C and the degree of tumor-specific CDK4/6 inhibition.
• To correlate the degree of dose-related tumor-specific CDK4/6 inhibition of FCN-437c and tumor response [ Time Frame: Baseline up to approximately 1 year ]
  Determine the association between FCN-437C antitumor activity and tumor-specific CDK4/6 inhibition
• To correlate the retinoblastoma (Rb) protein expression as a potential predictive biomarker to FCN-437c tumor response according to RECIST 1.1 criteria [ Time Frame: Baseline up to approximately 1 year ]
  To evaluate the proportion of patients expressing the retinoblastoma (Rb) protein with a reduction in tumor burden as defined by RECIST 1.1. criteria that may predict a response or resistance to FCN-437c treatment in solid tumors
• To correlate phosphorylated retinoblastoma (Rb) protein expression as a potential predictive biomarker for FCN-437c tumor response according to RECIST 1.1 criteria [ Time Frame: Baseline up to approximately 1 year ]
  To evaluate the proportion of patients expressing phosphorylated retinoblastoma (Rb) protein with a reduction in tumor burden as defined by RECIST 1.1. criteria that may predict a response or resistance to FCN-437c treatment in solid tumors

This research study is a Phase I clinical trial, which tests the safety of an investigational intervention and also tries to define the appropriate dose of the investigational intervention to use for further studies. "Investigational" means that the intervention is being studied.

In this research study, the investigators are evaluating a new drug, FCN-437c, as a potential new treatment for cancer.

The FDA (the U.S. Food and Drug Administration) has not approved FCN-437c as a treatment for any disease.

FCN-437c is a new generation CDK4/6 inhibitor. The CDK 4/6 inhibitors play a key role in regulating the transition from G1 to the S-phase of the cell cycle.

The cyclin D-cyclin dependent kinase (CDK) 4/6-inhibitor of CDK4 (INK4)-retinoblastoma (Rb) pathway controls cell cycle progression by regulating the G1-S checkpoint. Dysregulation of the cyclin D-CDK4/6-INK4-Rb pathway results in increased proliferation, and is frequently observed in many types of cancer. Due to the importance of CDK4/6 activity in cancer cells, CDK4/6 inhibitors have emerged as promising candidates for cancer treatment.

FCN-437c is a novel, potent and selective inhibitor of CDK4/6 exhibiting cellular potency against a number of human tumor cell lines.

Laboratory experiments show that FNC-437c may stop tumor growth.

The purposes of this study are:

• To evaluate the safety and tolerability of FCN-437c when administered orally to subjects with advanced solid tumors
• To determine the MTD and/or the Phase 2 Dose for FCN-437c

Inclusion Criteria:

1. Have given written informed consent prior to any study specific procedures
2. Male or female subject ≥ 18 years

3. Histologically/cytologically confirmed, unresectable locally advanced or metastatic solid tumors that are refractory to standard therapy or for which no standard therapy exists. Note for patients with non-small cell lung cancer [NSCLC] and patients with activating ALK translocation, or EFGR mutations must have been treated and failed appropriate targeted treatment).

   Subjects enrolled in cohort expansion at MTD should have specific tumor types as below:

   • KRAS mutant NSCLC confirmed by a documented historical report
   • Breast cancer previously treated with a CDK4/6 inhibitor

4. All subjects should have evaluable disease as per RECIST 1.1 (Eisenhauer, 2009).

   Subjects enrolled in cohort expansion at MTD should have measurable disease (presence of at least one measurable lesion) as per RECIST 1.1.

5. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) ≤ 1
6. Subjects with life expectancy of ≥ 3 months
7. Subjects with central nervous system (CNS) metatases are eligible if clinically controlled that is defined as surgical excision/and or radiation therapy followed by 3 weeks of stable neurologic function and no evidence of CNS disease progression as determined by contrast-enhanced computer tomography (CT) and nuclear magnetic resonance imaging (MRI) within 3 weeks prior to the first dose of study drug.

8. Must have adequate organ function, including the following:

   • Bone marrow reserve: absolute neutrophil count (ANC) ≥ 1.5 X 10 9/L; platelet count ≥ 100 x 10 9/L;hemoglobin ≥ 9g/dL or ≥ 5.6 mmol/L
   • Hepatic: total bilirubin ≤ 1.5 times the upper limit of normal (ULN), aspartate transaminase (AST) and/or alanine aminotransferase (ALT) ≤ 2.5 times ULN (< 5 times ULN if liver metastases).
   • Renal: estimated creatinine clearance ≥ 45 mL/min based on the Cockcroft-Gault equation (Appendix 19.4).
   • Coagulation: INR < 2.0, activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN.
9. Subjects are able to swallow capsules.
10. Subjects (women of child-bearing potential and males) should be willing to use viable contraception method that is deemed effective by the Investigator throughout the treatment period and for at least 3 months following the last dose of study drug. Postmenopausal women must have been amenorrheic for at least 12 months to be considered of non-childbearing potential.

Exclusion Criteria:

1. Females during pregnancy or breastfeeding.
2. Subjects on any anticancer therapy approved or experimental, including chemotherapy, immune therapy, radiation therapy, hormonal therapy (Exceptions: hormone-replacement therapy, testosterone or oral contraceptives), biologic therapy, within 3 weeks (or 5 half-lives whichever is shorter) prior to initiation of study treatment. Note: Subjects should be recovered from treatment related toxicity resolved to baseline except for residual alopecia.
3. Subjects who had prior treatment with a CDK4/6 inhibitor except Hormone receptor (HR)+/Human epidermal growth factor receptor 2 (HER2)- breast cancer patients who may have received CDK4/6 inhibitor as a standard treatment.
4. Subjects with history of gastric bypass surgery or banding procedure.
5. Subjects who have had major surgery within the 28-days from the screening or subjects who have undergone organ transplant surgery.
6. Active hepatitis B (HBV) or hepatitis C (HCV). HBV carriers without active disease (HBV DNA titer < 1000 cps/mL or 200 IU/mL), or cured HCV (negative HCV RNA test) may be enrolled. Subjects with controlled human immunodeficiency virus (HIV) disease may be eligible.
7. Subjects with a concomitant medical condition that would increase the risk of toxicity, in the opinion of the Investigator or Sponsor.
8. Unresolved toxicities (other than alopecia) from previous anti-cancer therapy defined as toxicities not resolved to NCI CTCAE Version 5.0, Grade ≤ 1.
9. Subject who have had severe infection within 4 weeks or signs and symptoms of any active infection within 2 weeks prior to the first dose administration.
10. Severe or uncontrolled cardiac disease requiring treatment, congestive heart failure New York Heart Association (NYHA) III or IV, unstable angina pectoris even if medically controlled, history of myocardial infarction during the last 3 months, serious arrhythmias requiring medication (with exception of atrial fibrillation or paroxysmal supraventricular tachycardia).
11. A resting ECG with QTcF ≥ 470 msc or the subject has a congenital prolonged QT syndrome or with concomitant medications known to prolong the QT interval.
12. Taking a prohibited concomitant medication or inability to follow concomitant medications guidelines
13. Any other serious underlying medical (e.g., uncontrolled diabetes mellitus, uncontrolled hypertension, active uncontrolled infection, active gastric ulcer, uncontrolled seizures, severe hearing impairment, cerebrovascular incidents, gastrointestinal bleeding, severe signs and symptoms of coagulation and clotting disorders, cardiac conditions), psychiatric, psychological, familial or geographical condition that, in the judgment of the Investigator, may interfere with the planned staging, treatment and follow-up, affect subject compliance or place the subject at high risk from treatment-related complications.