Patients who are currently receiving drugs that are strong or moderate inhibitors and/or inducers of cytochrome P, family , subfamily A, polypeptide (CYPA) or sensitive CYPA substrates and CYPA substrates with a narrow therapeutic range are not eligible; the use of aprepitant as an antiemetic is prohibited; caution should be exercised with concomitant administration of AZD (MK-) and agents that are sensitive substrates of cytochrome P, family , subfamily C, polypeptide (CYPC), C and C, or substrates of this enzyme with narrow therapeutic ranges, as well as agents that are inhibitors or substrates of permeability glycoprotein (P-gp) Currently receiving medications known to be inhibitors of CYPA/. Subjects currently receiving medications of known inducers of CYPA/ or substrates of CYPC/ and CYPA may be excluded. Inclusion Criteria for all Modules:\n\n . Metastatic MIBC\n\n . nd/rd line\n\n . Failed adjuvant/neo-adjuvant chemotherapy < yr\n\n . lesion ? mm at baseline in the longest diameter suitable for accurate repeated\n measurement\n\n . WHO perf. status -\n\n For Module A:\n\n . M/F ?\n\n . Confirmation of FGFR mutation or FGFR fusion\n\n For Module B:\n\n . Hgb ? g/dL\n\n . Deleterious mutation, deletion or truncation in any HRR genes\n\n For Module C:\n\n . Tumour harbours a deletion or inactivating mutation of the CDKNA or RB genes and/or\n amplification of CCNE, MYC, MYCL or MYCN genes\n\n For Module E:\n\n . Contraception must be sustained throughout treatment with vistusertib and wks after\n last dose\n\n For Module F:\n\n . Adequate organ and marrow function, defined as Leukocytes ?.x(exp)/L; ANC\n ?.x(exp)/L; platelets ?x(exp)/L\n\n . Contraceptive measures must be sustained throughout treatment with AZD and for \n days after the last dose.\n\n Exclusion Criteria for all Modules:\n\n . Immunotherapy, chemotherapy, anticancer agents, radiotherapy < wks, or radiotherapy\n for palliation < wks, any study drugs < days.\n\n . Major surgery < wk\n\n . Unresolved toxicities from prior therapy\n\n . Concurrent chemotherapy, immunotherapy, biologic or hormonal therapy\n\n . Immunosuppressive drugs < days\n\n . Any of the following: Autoimmune disease ? yr; IBD; primary immunodeficiency; organ\n transplant requiring immunosuppressives\n\n . Spinal cord compression or brain metastases, treated and stable & not requiring\n steroids for at least weeks\n\n . Severe or uncontrolled systemic disease\n\n . Any of the following: Mean QTc ? ms; abnormalities in resting ECG; factors that\n increase the risk of QTc prolongation or arrhythmia; uncontrolled hyper/hypotension;\n LVEF <%; atrial fibrillation; NYHA Grade II-IV; severe valvular disease;\n uncontrolled angina; stroke/TIA < months; acute coronary syndrome < months\n\n . Any of the following laboratory values: ANC <.x(exp)/L; Platelets\n .xULN or >xULN with liver mets; Total\n bilirubin >. times ULN or with Gilbert's disease ?ULN; Creatinine >.xULN\n concurrent with creatinine clearance < mL/min; Corrected Ca >ULN, PO >ULN\n\n . Active infection including tuberculosis, hepatitis B (HBV), hepatitis C (HCV), or\n human immunodeficiency virus. Patients with a past or resolved HBV infection are\n eligible. Patients positive for HCV antibody are eligible only if polymerase chain\n reaction is negative for HCV RNA.\n\n . Live attenuated vaccination < days\n\n For Module A:\n\n . Prior exposure to: Nitrosourea or mitomycin C < weeks; any agent with FGFR inhibition\n as its primary pharmacology; AZD; potent inhibitors/inducers of CYPA, inhibitors\n of CYPD or substrates of CYPA < wks\n\n . Ophthalmological criteria: RPED; laser treatment or intraocular injection for macular\n degeneration; age-related macular degeneration; retinal vein occlusion; retinal\n degenerative disease; other clinically relevant chorioretinal defect\n\n . Refractory nausea/vomiting, chronic GI diseases, or previous bowel resection\n\n For Module B:\n\n . Transfusion < days\n\n . Concurrent medications that are strong inhibitors of cytochrome P (CYP) A (CYPA)\n or strong inducers of CYPA.\n\n . Previous treatment with PARP inhibitor, including olaparib\n\n . Patients with history of MDS or AML\n\n For Module C:\n\n . Prior exposure to any of the following: Nitrosourea or mitomycin C < wks; any agent\n with Wee inhibition as its primary pharmacology; prior treatment with AZD\n\n . Any drugs or products known to be sensitive to CYPA substrates or CYPA substrates\n with narrow therapeutic index, or moderate to strong inhibitors/inducers of CYPA\n\n . Herbal preparations\n\n . Refractory nausea and vomiting or chronic GI diseases\n\n . Cardiac disease < months\n\n For Module E:\n\n . Minor surgery < days of first dose\n\n . Exposure to specific substrates of OATPB, OATPB, MATE and MATEK