Inclusion Criteria

          1. Patients ≥ 18 years of age.

          2. Histologically or cytologically confirmed diagnosis of solid malignancy, for which no
             standard curative or life prolonging therapy is available.

          3. Have an ECOG Performance Status of ≤ 1. Refer to Appendix 1.

          4. Life expectancy of ≥ 12 weeks.

          5. Adequate bone marrow, liver, and renal functions, defined as:

               -  Platelet count ≥ 100 x 109/L, absolute neutrophil count (ANC)

                  ≥ 1.5 x 109/L, Hemoglobin ≥ 9 g/dL.

               -  ALT and AST ≤ 2.5 upper limit normal (ULN), or < 5 x ULN if liver metastases are
                  present; serum total bilirubin ≤ ULN or 1.5 x ULN if liver metastases are present
                  or total 3 x ULN with direct bilirubin ≤ ULN in patients with well documented
                  Gilbert Syndrome.

               -  Serum Creatinine < 1.5 x ULN (upper limit of normal) or estimated creatinine
                  clearance ≥ 60 mL/min, as calculated using method standard for the institution
                  (Appendix 2).

          6. Glycated hemoglobin (HgbA1c) ≤ 7 %; Fasting Plasma Glucose (FPG) ≤ 7.0 mmol/L (125
             mg/dL).

          7. Women of childbearing potential must have a negative pregnancy test (urine or serum)
             performed within 7 days prior to the start of study drug.

          8. Able and willing to swallow and retain oral medication.

          9. Subject or legal representative must understand the investigational nature of this
             study and sign an Independent Ethics Committee/Institutional Review Board approved
             written informed consent form prior to receiving any study related procedure.

             Expansion part:

         10. Patients must have known PI3K/mTOR pathway gene aberrations (from molecular profiling
             studies).

         11. Patients must have HPV positive HNSCC containing activating PIK3CA mutations.

        Exclusion Criteria

          1. Concurrent or previous anti-cancer chemotherapy, immunotherapy or investigational
             agents < 3 weeks, or palliative radiation < 2 weeks prior to the first day of study
             treatment. Patients who receive gamma knife radiosurgery for brain metastases or whole
             brain radiation are eligible if gamma knife radiosurgery was performed > 2 weeks
             before treatment is started or whole brain radiation was performed > 4 weeks before
             treatment is started, and are clinically stable.

          2. Hormonal anticancer therapies except for LHRH antagonists or LHRH agonists in
             hormone-refractory prostate cancer

          3. Patient has a known hypersensitivity to any of the excipients of PQR309.

          4. Patient has had major surgery within 14 days prior to starting study drug or has not
             recovered from major side effects.

          5. Patients with poorly controlled diabetes mellitus, steroid-induced diabetes mellitus,
             HbA1c > 7%, or FPG > 7.0 mmol/L (125 mg/dL).

          6. Patients who are on (or will require) prolonged systemic corticosteroid treatment
             during the study, except for:

               -  if receiving corticosteroids, patients must have been on a stable or decreasing
                  dose of corticosteroids and no more than 1 mg of dexamethasone a day or
                  equivalent, i.e. 6 mg prednisone or 25 mg hydrocortisone for at least 5 days
                  prior to date of enrollment.

               -  a short duration (< 5 days) of systemic corticosteroids e.g., of chronic
                  obstructive pulmonary disease, or as an antiemetic corresponding at maximum to
                  the anti-inflammatory potency of 4 mg dexamethasone for treatment;

               -  topical applications for treatment of e.g., rash, inhaled sprays for treatment of
                  e.g., obstructive airways diseases, eye drops or local Protocol No. PQR309-003
                  Protocol Amendment 3, 23 September 2015 PIQUR Therapeutics AG - Confidential Page
                  15 of 108 injections (e.g., intra-articular);

          7. Patients who have taken herbal medications and certain fruits within 7 days prior to
             starting study drug, see section 11.1.2.7.

          8. Patients who have other concurrent severe and/or uncontrolled medical conditions that
             would, in the investigator's judgment, contraindicate patient participation in the
             clinical study (e.g., active or uncontrolled severe infection, chronic active
             hepatitis, immuno-compromised, acute or chronic pancreatitis, uncontrolled high blood
             pressure, interstitial lung disease, etc.).

          9. Patient has a known history of HIV infection (testing not mandatory).

         10. Patient has any of the following cardiac abnormalities:

               -  History of, or current, documented congestive heart failure (New York Heart
                  Association functional classification III - IV), documented cardiomyopathy.

               -  Left Ventricular Ejection Fraction (LVEF) < 40% as determined by Multiple Gated
                  Acquisition (MUGA) scan or echocardiogram (ECHO).

               -  Myocardial infarction ≤ 6 months prior to enrolment.

               -  Unstable angina pectoris.

               -  Serious uncontrolled cardiac arrhythmia.

               -  Symptomatic pericarditis.

         11. Patient has impairment of gastrointestinal (GI) function or GI disease that may
             significantly alter the absorption of study drug.

         12. Concomitant treatment with medicinal products that increase the pH (reduce acidity) of
             the upper gastrointestinal tract, including, but not limited to, proton-pump
             inhibitors (e.g. omeprazole), H2-antagonists (e.g. ranitidine) and antacids. Patients
             may be enrolled in the study after a wash-out period sufficient to terminate their
             effect.

         13. Patient has a history of non-compliance to medical regimen or inability to grant
             consent.

         14. Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a
             female after conception and until the termination of gestation, confirmed by a
             positive Human Chorionic Gonadotropin (hCG) laboratory test (> 5 mIU/mL). Patients
             with elevated hCG at baseline that is judged to be related to the tumor are eligible
             if hCG levels do not show the expected doubling when repeated 5 - 7 days later, or
             pregnancy has been ruled out by vaginal ultrasound.

         15. Patient who does not apply highly effective contraception during the study from
             screening until 90 days after discontinuing study treatment Protocol No. PQR309-003
             Protocol Amendment 3, 23 September 2015 PIQUR Therapeutics AG - Confidential Page 16
             of 108 (see section 11.3).

         16. Patients have any of the following mood disorders as judged by the Investigator or a
             Psychiatrist, or who meets the cut-off score of ≥ 12 the PHQ-9 or a cut-off of ≥ 15 in
             the GAD-7 mood scale, respectively, or selects a positive response of '1, 2, or 3' to
             question number 9 regarding potential for suicidal thoughts in the PHQ-9 (independent
             of the total score of the PHQ-9) see Appendix 4.

               -  Medically documented history of or active major depressive episode, bipolar
                  disorder (I or II), obsessive-compulsive disorder, schizophrenia, a history of
                  suicidal attempt or ideation, or homicidal ideation (immediate risk of doing harm
                  to others).

               -  ≥ CTCAE Grade 3 anxiety.

         17. Patients with a history of interstitial