Inclusion Criteria

          1. Part A (dose escalation):

             Patients with histologically or cytologically confirmed malignant advanced solid
             tumours refractory to standard therapy or for which no suitable effective standard
             therapy exists, including, but not limited to patients with PIK3CA mutant cancers, or
             those with somatic mutations or other aberrations known to result in a hyperactivated
             PI3K-AKT pathway.

             Advanced breast cancer with the following features:

               -  ER+ve breast cancer that has progressed on at least one line of prior endocrine
                  therapy, or

               -  PIK3CA mutant breast cancer progressed on at least one line of prior endocrine
                  therapy or chemotherapy

               -  breast cancer refractory to standard treatment

             Part B (dose expansion):

             Part B1 Patients with histologically or cytologically confirmed advanced ER+ve,
             HER2-ve breast cancer with a PIK3CA mutation confirmed by an accredited laboratory.

             Part B2

               -  Patients with histologically or cytologically confirmed advanced solid tumours
                  with mutations leading to a hyperactivated PI3K-AKT pathway, or other relevant
                  genetic aberrations; OR

               -  Patients with histologically or cytologically confirmed advanced ER-ve, HER2+ve
                  breast cancer with a PIK3CA mutation confirmed by an accredited laboratory; OR

               -  Patients with histologically or cytologically confirmed advanced triple negative
                  breast cancer with a PIK3CA mutation confirmed by an accredited laboratory.

             Part B3 Patients with histologically or cytologically confirmed advanced ER+ve,
             HER2-ve breast cancer.

             NB. PIK3CA mutation may be assessed in archival tumour samples, fresh tumour samples,
             or in circulating free DNA extracted from plasma or serum and the result must be from
             an accredited laboratory. This is mandatory for breast cancer patients in Part B1 and
             B2 and the result must be available prior to the patient entering the main study.

             A mutation will be considered pathogenic if described to be recurrent somatic mutation
             in COSMIC (http://cancer.sanger.ac.uk/cancergenome/projects/cosmic/). Other cancers
             with relevant genetic aberrations (e.g. KRAS mutations) may be considered, depending
             on emerging preclinical and clinical data on these novel antitumour agents.

          2. Prior cancer treatment as follows:

               -  Patients with ER+ve and HER2-ve breast cancer in Parts B1 and B3 should have
                  progressed on at least one prior hormone therapy and had a maximum of two prior
                  lines of chemotherapy for advanced breast cancer;

               -  Patients in the solid tumour AND triple negative breast cancer cohort of Part B2
                  must have progressed on at least one prior chemotherapy regimen for advanced
                  cancer;

               -  Patients with HER2+ve breast cancer in Part B2 should have progressed on at least
                  two prior HER2 directed therapies for advanced breast cancer (or one prior
                  therapy where no further HER2 directed therapy is available locally).

          3. Part A: Measurable disease as assessed by RECIST 1.1 OR evaluable disease. Part B1:
             Measurable disease as assessed by RECIST 1.1 Part B2 and B3: Measurable disease as
             assessed by RECIST 1.1 OR evaluable disease

          4. Life expectancy of at least 12 weeks

          5. World Health Organisation (WHO) performance status of 0-1 with no significant
             deterioration over the previous 2 weeks (Appendix 1)

          6. Haematological and biochemical indices within the ranges shown below. These
             measurements must be performed within one week (Day -7 to Day 1) before the patient
             goes in the trial.

        Laboratory Test Value required Haemoglobin (Hb) ≥ 10.0 g/dL Absolute neutrophil count ≥ 1.5
        x 109/L Platelet count ≥ 150 x 109/L Serum bilirubin ≤ 1.5 x upper limit of normal (ULN)
        except for patients with documented Gilberts' disease Alanine aminotransferase (ALT) and
        aspartate aminotransferase (AST) ≤ 2.5 x upper limit of normal (ULN) unless raised due to
        tumour in which case up to 5 x ULN is permissible

        Creatinine - If creatinine > 1.5 times ULN then: Either:

        Calculated creatinine clearance

        Or:

        Isotope clearance measurement

        ≤1.5 times ULN

          -  50 mL/min (uncorrected value)

          -  50mL/min (corrected) Coagulation INR <1.5, APTT <1.5x ULN

        Exclusion criteria:

          1. Radiotherapy (except for palliative reasons), endocrine therapy, immunotherapy or
             chemotherapy during the previous 4 weeks (6 weeks for nitrosoureas, Mitomycin-C) and 4
             weeks for investigational medicinal products before treatment

             Exceptions to this are:

               -  patients progressing on letrozole or fulvestrant;

               -  hormonal therapy with luteinizing hormone-releasing hormone (LHRH) analogues for
                  medical castration in patients with castrate resistant prostate cancer;

               -  bisphosphonates or RANK ligand antagonists that are permitted for the management
                  of bone metastases;

               -  palliative radiotherapy if given for bony metastases, as long as these are not
                  indicative of disease progression. Study drug must be stopped 3 days before
                  radiotherapy and restarted within 28 days, as long as bone marrow function has
                  returned to normal.

          2. Patients with prior exposure to either a CDK4/6 inhibitor OR a PI3K/ATK/mTOR inhibitor
             are excluded from the study With the exception of allosteric mTOR inhibitors such as
             everolimus that is allowed. Prior exposure to fulvestrant or aromatase inhibitors is
             permitted.

          3. Clinically significant abnormalities of glucose metabolism as defined by any of the
             following:

               -  Diagnosis of diabetes mellitus types I or II (irrespective of management).

               -  Glycosylated haemoglobin (HbA1C) ≥7.0% at screening

               -  Fasting Plasma Glucose ≥ 6.9mmol/L at screening. Fasting is defined as no caloric
                  intake for at least 8 hours.

          4. On-going toxic manifestations of previous treatments ≥ grade 1. Exceptions to this are
             alopecia or certain other toxicities, which in the opinion of the Investigator should
             not exclude the patient.

          5. History of malabsorption syndrome or other condition that would interfere with enteral
             absorption. For example active intestine inflammation (e.g., Crohn's disease or
             ulcerative colitis) requiring immunosuppressive therapy.

          6. History of inflammatory bowel disease (e.g. Crohn's disease or ulcerative colitis)

          7. Inability or unwillingness to swallow pills, or (for patients receiving fulvestrant)
             receive IM injections.

          8. Known untreated or active central nervous system (CNS) metastases (progressing or
             requiring corticosteroids for symptomatic control). Patients with a history of treated
             CNS metastases are eligible, provided they meet all of the following criteria:

               -  Evaluable or measurable disease outside the CNS is present.

               -  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 the baseline disease assessment for at least 28 days.

               -  Not requiring dexamethasone treatment.

          9. Major surgery (excluding minor procedures, e.g. placement of vascular access) within 4
             weeks of the first dose of study treatment.

         10. Ability to become pregnant (or already pregnant or lactating). However, those female
             patients who have a negative serum or urine pregnancy test before enrolment and agree
             to use two highly effective forms of contraception (oral, injected or implanted
             hormonal contraception and condom, have an intra-uterine device and condom, diaphragm
             with spermicidal gel and condom) for four weeks before entering the trial, during the
             trial and for six months afterwards are considered eligible.

         11. Male patients with partners of childbearing potential (unless they agree to take
             measures not to father children by using one form of highly effective contraception
             [condom plus spermicide] during the trial and for six months afterwards). Men with
             pregnant or lactating partners should be advised to use barrier method contraception
             (for example, condom plus spermicidal gel) to prevent exposure to the foetus or
             neonate.

             NB: Male patients who are potentially fertile should be made aware that palbociclib
             causes testicular degeneration in animal models and may wish to consider sperm
             preservation prior to beginning therapy.

         12. At high medical risk because of severe or uncontrolled systemic disease, such as:

             uncontrolled hypertension, symptomatic congestive heart failure ≥ class 2 (refer to
             appendix 4 for grading), unstable angina pectoris, stroke or myocardial infarction
             within 6 months, serious cardiac arrhythmia requiring treatment, with the exceptions
             of atrial fibrillation and paroxysmal supraventricular tachycardia or conduction
             abnormality that has been treated and for which the patient is no longer at risk for
             serious arrhythmia (e.g., Wolff-Parkinson-White syndrome treated with surgical
             ablation).

         13. Clinically significant history of liver disease, including cirrhosis, current alcohol
             abuse, or current known active infection with hepatitis B virus, or hepatitis C virus.

             Active infection is defined as requiring treatment with antiviral therapy or presence
             of positive test results for Hepatitis B (Hepatitis B surface antigen [HBsAg] and/or
             total Hb core antibody [anti-HBc]) or Hepatitis C (Hepatitis C virus [HCV] antibody).
             Unless required by local regulations, patients are not required to have HIV, HCB, or
             HCV assessments at screening if these assessments have not been previously performed.

             Patients who are positive for anti-HBc are eligible only if testing is also positive
             for Hepatitis B surface antibody [HbsAb] and polymerase chain reaction (PCR) is
             negative for HBV DNA.

             Patients who are positive for HCV serology are eligible only if testing for HCV RNA is
             negative.

         14. Immunocompromised status due to current known active infection with HIV or due to the
             use of immunosuppressive therapies for other conditions.

         15. Need for current chronic corticosteroid therapy, specifically dexamethasone or ≥ 10 mg
             of prednisone per day or an equivalent dose of other anti-inflammatory
             corticosteroids. Stable use (i.e., no change in dose within 1 month prior to Day 1 of
             Cycle 1) of inhaled corticosteroids is allowed.

         16. Prior bone marrow transplant or extensive radiotherapy to greater than 25% of bone
             marrow within eight weeks.

         17. Is a participant or plans to participate in another interventional clinical trial,
             whilst taking part in this Phase I study. Participation in an observational trial
             would be acceptable.

         18. Current malignancies of other types, with the exception of adequately treated
             cone-biopsied in situ carcinoma of the cervix uteri and basal or squamous cell
             carcinoma of the skin. Cancer survivors, who have undergone potentially curative
             therapy for a prior malignancy, have no evidence of that disease for 3 years or more
             and are deemed at negligible risk for recurrence, are eligible for the trial.

         19. Patients who require daily supplemental oxygen

         20. Any other condition which in the Investigator's opinion would not make the patient a
             good candidate for the clinical trial.