Study of AZD4956 as Monotherapy and in Combination With Anti-Cancer Agents in Participants With Advanced/Metastatic Homologous Recombination Deficient Solid Tumours

Core Inclusion Criteria: * Documented locally advanced or metastatic solid tumour malignancy. * Eastern cooperative oncology group (ECOG) performance status of 0 or 1 with no deterioration over the previous 2 weeks prior to screening and first day of dosing. * Minimum life expectancy ≥ 12 weeks. * Adequate organ and marrow function. * Female participants must not breastfeed and must not donate or retrieve ova for their own use from screening to approximately 6 months after the last dose of study intervention. Module 1 Inclusion Criteria: * Demonstrated evidence of disease progression. * Participants must have advanced or metastatic solid tumours. * Participants may have received up to one prior line of therapy with a poly (adenosine diphosphate-ribose) polymerase inhibitor (PARPi)-based regimen (either as a treatment or as maintenance). Module 2 Inclusion Criteria: Part A (AZD4956 in Combination with Saruparib Dose Escalation) and Part A-PD (PD Backfill Cohorts): * Participants must have one of the following conditions- 1. Histologically or cytologically confirmed carcinoma of the breast with recurrent locally advanced or metastatic disease and evidence of a predicted loss of function germline or somatic mutation. 2. Histologically or cytologically confirmed advanced ovarian, fallopian tube, or primary peritoneal cancer. 3. Histologically or cytologically confirmed adenocarcinoma of the prostate and advanced/metastatic castrate resistant prostate cancer (CRPC). 4. Histologically or cytologically confirmed advanced/metastatic pancreatic cancer. * Participants must have evaluable disease. * Participants in PD backfill cohorts must not have received prior therapy with a PARPi-based regimen (either as a treatment or as maintenance). Part A (PD Backfill Cohorts) - Participants Undergoing Paired Biopsies: \- Participants must have a tumour suitable for biopsy. Part A-Non-PD (Non-PD Backfill Cohorts) and Part B (Dose Expansion Cohorts): * Participants must have histologically or cytologically confirmed adenocarcinoma of the prostate and advanced/metastatic CRPC. * Participants must have documented metastatic disease by clear evidence of ≥ 1 bone lesion (defined as one lesion with positive uptake on bone scan) and/or ≥ 1 soft tissue lesion (measurable or non-measurable). * Participants must have received the prior approved systemic therapies for metastatic prostate cancer. * Participants must not have received prior therapy with a PARPi-based regimen (either as a treatment or as maintenance). Core Exclusion Criteria: * Any significant laboratory finding or any severe and uncontrolled medical condition. * Participants with any known predisposition to bleeding. * Spinal cord compression or symptomatic and unstable brain metastases or leptomeningeal disease. * Allogenic organ transplantation. * Known to have active infection, including hepatitis B virus (HBV) or hepatitis C virus (HCV). * Known history of infection with human immunodeficiency virus (HIV). * Active gastrointestinal disease or other condition that will interfere significantly with the swallowing, absorption, distribution, metabolism or excretion of oral therapy. * Participants with history of myelodysplastic syndrome (MDS)/acute myeloid leukaemia (AML) or with features suggestive of MDS/AML. * Participants with a known hypersensitivity to the investigational product(s) or any of the excipients of the product(s). * Previous dosing with AZD4956.