Inclusion Criteria:

          1. Written informed consent prior to admission to this study

          2. Age ≥18 years

          3. ECOG performance status 0 or 1

          4. Life expectancy ≥12 weeks

          5. Patients must have at least one lesion, not previously irradiated, that can be
             measured accurately at baseline as ≥10 mm in the longest diameter (except lymph nodes
             which must have short axis ≥15 mm) with computed tomography (CT) or magnetic resonance
             imaging (MRI) which is suitable for accurate repeated measurements

          6. Radiological or clinical evidence of disease progression

          7. Formalin fixed, paraffin embedded tumour sample from the primary or recurrent cancer
             must be available for central testing

          8. Adequate haematologic and end organ function, defined by the following laboratory
             results obtained within 7 days prior to the first study treatment:

               -  ANC ≥ 1.5 x 109/l (without granulocyte colony-stimulating factor support within 2
                  weeks prior to the first study treatment)

               -  Platelet count ≥ 100 x 109/l (without transfusion within 2 weeks prior to the
                  first study treatment)

               -  Haemoglobin ≥ 9 g/dl (transfusion permitted to establish target haemoglobin
                  levels prior to the first study treatment)

               -  Serum creatinine ≤1.5 times the upper limit of normal (ULN) or calculated
                  creatinine clearance ≥ 50 ml/min

               -  Bilirubin level ≤1.5 x ULN (patients with known Gilbert disease who have
                  bilirubin levels ≤ 3 x ULN may be enrolled)

               -  AST or ALT <2.5 x ULN or <5 x ULN in the presence of liver metastases

               -  Alkaline phosphatase (ALP) <2.5 x ULN or <5 x ULN in the presence of liver and/or
                  bone metastases

               -  INR and aPTT ≤1.5 x ULN; this applies only to patients who are not receiving
                  therapeutic anticoagulation; patients receiving therapeutic anticoagulation
                  should be on a stable dose.

               -  Female patients of child-bearing potential are eligible, provided they have a
                  negative serum or urine pregnancy test within 2 weeks prior to the first dose of
                  study treatment, preferably as close to the first dose as possible. All patients
                  with reproductive potential must agree to use adequate contraception beginning
                  two weeks before the first dose of investigational product and for three months
                  after the discontinuation of treatment. Adequate contraception methods include:
                  intrauterine device [IUD], birth control pills unless clinically contraindicated,
                  or a barrier device.

        Inclusion Criteria unique to the Dose Escalation Part (phase Ib part):

          1. Histologically or cytologically advanced solid tumour limited to:

               -  Tumour types with frequent activation of MAPK and/or PI3K pathways (pancreatic,
                  thyroid, endometrial, renal, breast or ovarian carcinoma, colorectal cancer,
                  NSCLC or melanoma) OR

               -  Tumours with known alteration in ≥1 gene involved in PI3K/AKT/mTOR or Ras/MEK
                  pathway signalling, such as: KRAS, NRAS, BRAF, PIK3CA, PTEN, AKT, LKB1, EGFR,
                  FGFR, HER2, MET, RET, KIT, NF1

          2. Metastatic or locally advanced disease, which is refractory to conventional treatment
             or for which no conventional therapy exists; locally recurrent disease must not be
             amenable to resection with curative intent (patients who are considered suitable for
             surgical or ablative techniques following potential down-staging with study treatment
             are not eligible).

        Inclusion Criteria unique to the lung cancer dose expansion cohorts (phase IIa part):

          1. Histologically confirmed NSCLC

          2. Stage III disease that is unsuitable to radio-chemotherapy or Stage IV disease or
             recurrent NSCLC; recurrent disease must not be amenable to resection or radical
             radiotherapy with curative intent.

          3. Prior chemotherapy and/or, if indicated/accessible, EGFR-directed or ALK-directed
             therapy for advanced disease

        Inclusion Criteria unique to the TNBC dose expansion cohort (Phase IIa):

          1. Histologically confirmed TNCB defined as tumour cells being:

               -  Negative for ER with <1% of tumour cells positive for ER on IHC or IHC score
                  (Allred) of ≤2

               -  Negative for PR with <1% of tumour cells positive for PR on IHC or IHC score
                  (Allred) of ≤2 or PR unknown, and

               -  Negative for HER2 with 0, 1+ or 2+ intensity on IHC and no evidence of
                  amplification on ISH.

          2. Metastatic or locally recurrent disease; locally recurrent disease must not be
             amenable to resection with curative intent (patients who are considered suitable for
             surgical or ablative techniques following potential down-staging with study treatment
             are not eligible).

          3. Prior chemotherapy for advanced disease

        Exclusion Criteria:

          1. Symptomatic CNS involvement or CNS involvement requiring steroid therapy; patients
             with treated brain metastases that are asymptomatic and have been clinically stable
             for 1 month will be eligible for protocol participation

          2. Prior chemotherapy, biological therapy, radiation therapy, immunotherapy, other
             anticancer agents and any investigational agents within 14 days of starting study
             treatment (not including palliative radiotherapy at focal sites)

          3. Any unresolved toxicity > CTCAE Grade 1 from previous anti-cancer therapy, with the
             exception of alopecia

          4. Current refractory nausea and vomiting, chronic gastrointestinal disease or inability
             to swallow the formulated product or previous significant bowel resection that would
             preclude adequate absorption of the study medication

          5. Significant cardiovascular disease, such as;

               -  History of myocardial infarction, acute coronary syndromes (including unstable
                  angina), or coronary angioplasty/stenting/bypass grafting within past 6 months.

               -  Uncontrolled angina (Canadian Cardiovascular Society grade II-IV despite medical
                  therapy)

               -  History of symptomatic congestive heart failure (CHF) New York Heart Association
                  (NYHA) Classes II-IV or Left ventricular ejection fraction (LVEF) <55% measured
                  by echocardiography

               -  Severe cardiac arrhythmia requiring medication or severe conduction abnormalities
                  (unless compensated by ventricular pacemaker); atrial fibrillation with a
                  ventricular rate >100 bpm on ECG at rest

               -  Poorly controlled hypertension (resting diastolic blood pressure >115 mmHg)

               -  Clinically significant valvular disease, cardiomegaly, ventricular hypertrophy,
                  or prior or current cardiomyopathy

          6. QTc prolongation defined as a QTc interval >470 msecs

          7. Concomitant medications known to prolong QT interval

          8. Patients receiving concomitant immunosuppressive agents or chronic systemic
             corticosteroids (≥ 10 mg prednisolone or an equivalent dose of other anti-inflammatory
             corticosteroids) use for ≥ 28 days at the time of study entry except in cases outlined
             below: Topical applications (e.g. rash), inhaled sprays (e.g. obstructive airways
             diseases), eye drops or local injections (e.g. intra-articular) are allowed. Patients
             on stable low dose (<10 mg prednisolone or an equivalent dose of other
             anti-inflammatory corticosteroids) of corticosteroids for at least two weeks before
             registration are allowed

          9. Evidence of interstitial fibrotic lung disease (bilateral, diffuse, parenchymal lung
             disease)

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

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

               -  Glycosylated haemoglobin (HbA1C) ≥ 8.0% at screening (64 mmol/mol) (conversion
                  equation for HbA1C [IFCC-HbA1C (mmol/mol) = [DCCT-HbA1C (%) - 2.15] x 10.929)

               -  Fasting Plasma Glucose ≥ 7.0mmol/L (126 mg/dL) at screening. Fasting is defined
                  as no caloric intake for at least 8 hours.

         11. Ophthalmological conditions as follows:

               -  Intra-ocular pressure >21 mmHg, or uncontrolled glaucoma (irrespective of
                  intra-ocular pressure)

               -  Current or past history of central serous retinopathy or retinal vein occlusion

         12. Exposure to potent or moderate inhibitors or inducers of CYP3A4/5 if taken within the
             stated washout periods before the first dose of study treatment

               -  Inhibitors (competitive): ketoconazole, itraconazole, indinavir, saquinovir,
                  nelfinavir, atazanavir, amprenavir, fosamprenavir, troleandomycin, telithromycin,
                  fluconazole, nefazodone, cimetidine, aprepitant, miconazole, fluvoxamine,
                  P-glycoprotein, grapefruit juice, or seville oranges (1 week minimum wash-out
                  period), amiodarone (27 week minimum wash-out period)

               -  Inhibitors (time dependent): erythromycin, clarithromycin, verapamil, ritonavir,
                  diltiazem (2 week minimum wash-out period)

               -  Inducers: phenytoin, rifampicin, St. John's Wort, carbamazepine, dexamethasone,
                  primidone, griseofulvin, carbamazepine, barbiturates, troglitazone, pioglitazone,
                  oxcarbazepine, nevirapine, efavirenz, rifabutin (3 week minimum wash-out period)
                  and phenobarbitone (5 week minimum wash-out period)

         13. Exposure to potent or moderate inhibitors or inducers of CYP2C8 within the stated
             washout periods before the first dose of study treatment

               -  Inhibitors: Gemfibrozil, trimethoprim, glitazones, montelukast, quercetin (1 week
                  minimum wash-out period)

               -  Inducers: Rifampicin (3 week minimum wash-out period)

         14. Exposure to sensitive or narrow therapeutic range substrates of the drug metabolising
             enzymes CYP2C8, CYP2C9, CYP2C19, CYP2D6 or the drug transporters Pgp (MDR1) and BCRP
             within the appropriate wash-out period before the first dose of study treatment

         15. Active second malignancy (except non-melanomatous skin cancer): active secondary
             malignancy is defined as a current need for cancer therapy or a high possibility
             (>30%) of recurrence during the study.

         16. Any evidence of severe or uncontrolled systemic disease, active infection, active
             bleeding diatheses or renal transplant, including any patient known to have hepatitis
             B, hepatitis C or human immunodeficiency virus (HIV)

         17. Any other disease, metabolic dysfunction, physical examination finding, or clinical
             laboratory finding that, in the investigator's opinion, gives reasonable suspicion of
             a disease or condition that contraindicates the use of an investigational drug, may
             affect the interpretation of the results, render the patient at high risk from
             treatment complications or interferes with obtaining informed consent.

         18. Psychological, familial, sociological or geographical conditions that do not permit
             compliance with the study protocol.

         19. Concurrent treatment with other experimental drugs or participation in another
             clinical trial with any investigational drug ≤30 days prior to study entry depending
             on the half-life of the investigational drug and/or guidance issued by the TORCMEK IMP
             manufacturer. Please contact the TORCMEK Coordinating team for further information.

        Exclusion Criteria unique to the dose expansion cohorts (phase IIa part):

          1. Prior treatment with PI3K inhibitors, AKT inhibitors, mTOR inhibitors or MEK, Ras or
             Raf inhibitors.

          2. Prior radiotherapy to the indicator lesion(s); Newly arising lesions in previously
             irradiated areas are accepted.