Inclusion Criteria:

- Males and females >=18 years of age (at the time consent is obtained)

- Capable of giving signed informed consent

- Able to swallow and retain orally-administered medication

- Eastern cooperative oncology group (ECOG) performance status of 0 or 1

- Diagnosis of one of the following: 1. Part 1: Histologically- or cytological-confirmed diagnosis of non-resectable or metastatic solid malignancy. At the time of enrollment, subjects either: have progressed on prior therapy (radiographic documentation of progression is adequate for study participation) AND have no standard-of-care therapy that would be expected to achieve a durable clinical response, OR refuse standard therapy, OR are not candidates for standard therapy, OR have a disease for which no generally-accepted standard-of-care exists. 2. Part 2: Histologically- or cytologically-confirmed diagnosis of metastatic or non-resectable triple-negative breast cancer (TNBC) (estrogen receptor [ER]-/ progesterone receptor [PR]-/Human Epidermal Growth Factor Receptor 2 [Her2]-, as defined by local laboratory standards); metastatic or non-resectable transitional cell carcinoma of the bladder, ureter, or renal pelvis; recurrent GBM; or non-Hodgkin's lymphoma. At the time of enrollment, subjects either: have progressed on prior therapy (radiographic documentation of progression is adequate for study participation) AND have no standard-of-care therapy that would be expected achieve a durable clinical response, OR refuse standard therapy, OR are not candidates for standard therapy.

- Evaluable disease: 1. During Part 1, evaluable disease is required; measurable disease per RECIST v1.1 is recommended but not required, 2. Subjects enrolled in Part 2 must demonstrate measurable disease per the disease-specific criteria.

- PK/PD/biomarker/metabolite expansion cohort(s) only: Subjects must consent to pre- and post-dose tumor biopsies and additional sample collection procedures.

- All prior treatment-related toxicities must be National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) v4 =< Grade 1 (except alopecia [permissible at any Grade] and peripheral neuropathy [which must be =< Grade 2]) at the time of treatment allocation.

- Adequate organ function as per Hematologic, Hepatic, Renal and Cardiac Laboratory Values

- Reproductive criteria: 1. A male subject with female partner of child bearing potential must agree to use one of the methods of contraception for the duration specified in protocol. 2. A female subject is eligible to participate if she is not pregnant (as confirmed by a negative serum human chorionic gonadotrophin [hCG] test), not nursing, and at least one of the following conditions apply: Reproductive potential: subject must agree to follow one of the options and the duration specified in protocol; Non-reproductive potential defined as i) Pre-menopausal females with one of the following: Documented tubal ligation, Documented hysteroscopic tubal occlusion procedure with follow-up confirmation of bilateral tubal occlusion, Hysterectomy, Documented Bilateral Oophorectomy; ii) Postmenopausal defined as 12 months of spontaneous amenorrhea with an appropriate clinical profile or females over 60 years of age. Females on hormone replacement therapy (HRT) and whose menopausal status is in doubt will be required to use one of the highly effective contraception methods if they wish to continue their HRT during the study. Otherwise, they must discontinue HRT to allow confirmation of post-menopausal status prior to study enrollment.

Exclusion Criteria:

- Malignancy attributed to prior solid organ transplant

- Symptomatic or untreated leptomeningeal or brain metastases or spinal cord compression. Subjects previously treated for these conditions that have had stable central nervous system (CNS) disease (verified with consecutive imaging studies) for >1 month , are asymptomatic and off corticosteroids, or are on stable dose of corticosteroids for at least 1 month prior to study Day 1 are permitted. Stability of brain metastases must be confirmed with imaging. Subject treated with gamma knife therapy can be enrolled 2 weeks post-procedure as long as there are no post-procedure complications/they are stable. In addition, subjects treated or currently taking enzyme-inducing anticonvulsant (EIAC) are allowed on study. This criterion does not apply to subjects in the Part 2 GBM cohort

- Recent prior therapy, defined as 1. Any non-monoclonal anti-cancer therapy within 14 days or 5 half-lives, whichever is longer, prior to the first dose of GSK3326595. Any nitrosoureas or mitomycin C within 42 days prior to the first dose of GSK3326595. Prior therapy with biologic agents (including monoclonal antibodies) is permitted so long as 28 days have elapsed since therapy and all therapy-related AEs have resolved to =< Grade 1, 2. Any radiotherapy within 14 days or major surgery within 28 days prior to the first dose of GSK3326595. For subjects in the GBM cohort, subjects must have completed radiation therapy at least 28 days prior to the first dose of GSK3326595. 3. Anti-androgen therapies for prostate cancer, such as bicalutamide, must be stopped 4 weeks prior to enrollment. Second-line hormone therapies such as enzalutamide or abiraterone should be stopped 2 weeks prior to enrolment. Subjects with prostate cancer should remain on luteinizing hormone releasing hormone (LHRH) agonists or antagonists. Subjects with prostate cancer may also remain on low-dose prednisone or prednisolone [up to 10 milligram (mg)/day] and still be eligible for this study.

- History of a second malignancy, excluding non-melanoma skin cell cancer, unless that malignancy was treated definitively and has not recurred for at least three years.

- Current use of a prohibited medication or planned use of any forbidden medications during treatment with GSK3326595.

- Evidence of severe or uncontrolled systemic diseases (e.g., unstable or uncompensated respiratory, hepatic, renal, cardiac disease, or clinically significant bleeding episodes). Any serious and/or unstable pre-existing medical (aside from malignancy), psychiatric disorder, or other conditions that could interfere with subject's safety, obtaining informed consent or compliance to the study procedures, in the opinion of the Investigator.

- Any clinically significant gastrointestinal (GI) abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach and/or bowels.

- History of known human immunodeficiency virus (HIV) infection or positive HIV test result at screening.

- Presence of hepatitis B surface antigen (HBsAg) or positive hepatitis C antibody test result at screening or within 3 months prior to first dose of study treatment. Subjects with positive Hepatitis C antibody due to prior resolved disease can be enrolled only if a confirmatory negative Hepatitis C RNA polymerase chain reaction (PCR) is obtained.

- Any of the following cardiac abnormalities: 1. History of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within the past 6 months prior to first dose of study drug. 2. Presence of a cardiac pacemaker, 3. Baseline Corrected QT (Fridericia's formula) interval (QTcF) >=450 millisecond (msec), 4. Uncontrolled arrhythmias. Subjects with rate-controlled atrial fibrillation for >1 month prior to first dose of study drugs may be eligible. 5. Class II, III or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system.

- History of sensitivity to any of the study medications, or components thereof or a history of drug or other allergy that, in the opinion of the investigator or Medical Monitor, contraindicates their participation.