Key Inclusion Criteria:

          -  Fully understand the study and voluntarily sign the ICF;

          -  ≥18years of age;

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1;

        Dose Escalation Phase:

        • Histologically or cytologically documented, locally advanced or metastatic solid
        malignancy of any type (except squamous NSCLC) that has progressed on approved systemic
        therapy, and for whom no effective therapy or standard of care exists. This cohort is
        closed to enrollment.

        Dose Expansion Phase:

          -  Cohort A: Histologically or cytologically documented, locally advanced or metastatic
             solid malignancy of any type (except squamous NSCLC), that has progressed on approved
             systemic therapy, and for whom no effective therapy or standard of care exists. This
             cohort is closed to enrollment.

          -  Cohort B: Histologically or cytologically documented mCRC in patients that have
             progressed on, or had intolerable toxicity with at least 1 FDA-approved third-line
             systemic therapy (trifluridine/tipiracil or regorafenib). Patients must also have been
             previously treated with fluoropyrimidine-, oxaliplatin-, and irinotecan-based
             chemotherapy, an anti-VEGF biological therapy, and an anti-EGFR therapy for patients
             who had RAS wild-type tumors. This cohort is currently enrolling.

          -  Cohort C: Histologically or cytologically documented adenocarcinoma of the colon or
             rectum. Patients must have progressed on, or had intolerable toxicity to, at least 2
             prior regimens of standard chemotherapy, but must not have received prior TAS-102 or
             regorafenib. Prior therapy could have included adjuvant chemotherapy if a tumor had
             recurred within 6 months after the last administration of treatment. Patients must
             have been previously treated with fluoropyrimidine-, oxaliplatin-, and
             irinotecan-based chemotherapy, an anti-VEGF biological therapy and, if RAS wild-type,
             an anti-EGFR therapy

          -  Cohort D only: Histologically- or cytologically-confirmed Her2-negative, hormone
             receptor positive (ER+ and/or PR+) breast cancer

          -  Cohort E only: Histologically- or cytologically- confirmed triple negative breast
             cancer

        Key Exclusion Criteria:

        Patients will be excluded from the study, if any of the following criteria is met:

          -  Severe anemia, neutropenia, thrombocytopenia

          -  Moderate to severe renal or hepatic impairment

          -  Uncontrolled hypertension

          -  Risk of, or active hemorrhage: history or presence of active gastric/duodenal ulcer or
             ulcerative colitis, active hemorrhage of an unresected gastrointestinal tumor, history
             of perforation of fistulas; or any other condition that could possibly result in
             gastrointestinal tract hemorrhage or perforation within 6 months prior to screening;

          -  History of a thromboembolic event (including deep vein thrombosis [DVT], pulmonary
             embolism, stroke and/or transient ischemic attack) within 6 months prior to screening;

          -  Patients with squamous NSCLC;

          -  Clinically significant cardiovascular disease, including but not limited to acute
             myocardial infarction or coronary artery bypass surgery within 6 months prior to
             enrollment, severe or unstable angina pectoris, New York Heart Association Class
             III/IV congestive heart failure, ventricular arrhythmias requiring treatment, or left
             ventricular ejection fraction (LVEF) <50%;

          -  Patients who have ever received a VEGFR inhibitor, except for patients with mCRC
             enrolled in the dose expansion phase;

          -  Systemic anti-neoplastic therapies or any investigational therapy within 4 weeks prior
             to the first dose of study drug, including chemotherapy, radical radiotherapy,
             hormonotherapy, biotherapy and immunotherapy;

          -  Systemic small molecule targeted therapies (eg, tyrosine kinase inhibitors) within 5
             half-lives or 4 weeks (whichever is shorter) prior to the first dose of study drug;

          -  Palliative radiotherapy for bone metastasis/lesion within 2 weeks prior to the
             initiation of study drug;

          -  Brachytherapy (ie, implantation of radioactive seeds) within 60 days prior to the
             first dose of study drug;

          -  Known human immunodeficiency virus (HIV) infection;

          -  Known clinically significant history of liver disease, including cirrhosis, current
             alcohol abuse or active viral hepatitis. For patients with evidence of chronic
             hepatitis B (HBV), the HBV viral load must be undetectable on suppressive therapy, if
             indicated. Patients with a history of hepatitis C virus (HCV) infection must have been
             treated and cured. For patients with HCV who are currently on treatment, they are
             eligible if they have an undetectable HCV viral load;

          -  Tumor invasion of a large vascular structure, eg, pulmonary artery, superior or
             inferior vena cava.;

          -  Women who are pregnant or lactating;

          -  Brain metastases and/or spinal cord compression untreated with surgery and/or
             radiotherapy, and without clinical imaging evidence of stable disease for 14 days or
             longer; patients requiring steroids within 4 weeks prior to start of study treatment
             will be excluded;

          -  No other malignancy, except for non-melanoma skin cancer, during the 5 years prior to
             screening;

          -  Inability to take medication orally, dysphagia or an active gastric ulcer resulting
             from previous surgery (eg, gastric bypass) or a severe gastrointestinal disease, or
             any other condition that investigators believe may affect absorption of the
             investigational product;

          -  Other disease, metabolic disorder, physical examination anomaly, abnormal laboratory
             result, or any other condition that investigators suspect may prohibit use of the
             investigational product, affect interpretation of study results, or put the patient at
             undue risk of harm based on the investigator's assessment;

          -  Known hypersensitivity to fruquintinib or any of its excipients.

          -  For Cohort C only: patients who have been previously treated with TAS-102 or
             regorafenib