General Inclusion Criteria:  Signed written informed consent Discontinued all previous treatments for cancer for at least 21 days or 5 half-lives, whichever is shorter, and recovered from the acute effects of therapy. Palliative radiotherapy must have completed 1 week prior to start of study treatment. At least 1 radiologically evaluable lesion (measurable and/or non-measurable) that can be assessed at baseline and is suitable for repeated radiological evaluation by RECIST v1.1 or Prostate Cancer Working Group-3 (PCWG-3) Acceptable hematologic, renal, hepatic, and coagulation functions independent of transfusions and granulocyte colony-stimulating factor Female patients of childbearing potential and male patients with female partners of childbearing potential are required to use highly effective contraception plus one barrier method for up to 4 weeks for females and 16 weeks for males in Parts A1/B1/B2 or 7 months for all patients in Parts A2/B3 following the last dose of study treatment. Male patients are required to refrain from donating sperm for up to 16 weeks (Part A1/B1/B2) or 7 months (Part A2) following the last dose of study treatment. Estimated life expectancy of ≥12 weeks  Additional inclusion criteria for participants in dose escalation (Part A1):  Advanced or metastatic cancer, which is refractory to standard therapies, or for which no standard therapies exist, or for which the investigator feels no other active therapy is required for the duration of the study Non-irradiated tumor tissue sample (archival or newly obtained core biopsy of a tumor lesion) available for submission for analysis  Additional inclusion criteria for participants in dose escalation (Part A2):  • Advanced or metastatic cancer for which a PARP inhibitor is an appropriate treatment option. Participants may have received prior treatment with talazoparib or another PARP inhibitor.  Additional inclusion criteria for participants in dose expansion (Part B1):  Advanced or metastatic solid tumors that have undergone disease progression during treatment with a PARP inhibitor for an approved indication At least 1 measurable lesion assessable using standard techniques by RECIST v1.1 or PCWG-3 guidelines Non-irradiated, biopsiable tumor lesion  Additional inclusion criteria for participants in dose expansion (Part B2):  Advanced or metastatic cancer that is refractory to standard therapies, or for which no standard therapies exist, or for which the investigator feels no other active therapy is required for the duration of the study with characteristics indicative of sensitivity to pol theta inhibition No prior treatment with a PARP inhibitor and must not have a disease for which there is an approved PARP inhibitor At least 1 measurable lesion assessable using standard techniques by RECIST v1.1 or PCWG-3 guidelines  Additional inclusion criteria for participants in dose expansion (Part B3):  HER2-negative locally advanced or metastatic breast cancer Deleterious or suspected deleterious germline BRCA1 or BRCA2 mutation No more than 3 prior chemotherapy-inclusive regimens (including antibody conjugates) Prior treatment with a taxane or anthracycline unless contraindicated No prior treatment with a PARP inhibitor At least 1 measurable lesion assessable using standard techniques by RECIST v1.1  General Exclusion Criteria:  Women who are pregnant, breast feeding, or who plan to become pregnant while in the study or within 4 weeks after the last administration of ART4215 or within 7 months after the last administration of talazoparib Men who plan to father a child while in the study or within 16 weeks after the last administration of ART4215 (Part A1/B1/B2) or within 7 month after the last administration of study treatment (Part A2/B3). Serious concomitant systemic disorder that would compromise the participants ability to adhere to the protocol including: opportunistic HIV/AIDs-related infection(s) within the past 12 months, hepatitis B virus, or hepatitis C virus; known history of clinical diagnosis of tuberculosis; malignancy prior to the one currently being treated [including myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML)] that is not in remission Have MDS/AML or features suggestive of MDS/AML Interstitial lung disease or pneumonitis Moderate or severe cardiovascular disease Symptomatic or uncontrolled brain metastases, spinal cord compression, or leptomeningeal disease requiring concurrent treatment; stable brain metastases are eligible Received a live vaccine within 30 days before the first dose of study treatment History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study, or is not in the best interest of the patient to participate Recent major surgery within 4 weeks prior to entry into the study or minor surgery within 1 week of entry into the study Significant bleeding disorder or vasculitis or had a Grade ≥3 bleeding episode within 12 weeks prior to enrollment Currently enrolled in a clinical trial involving an investigational product or any other type of medical research judged not to be scientifically or medically compatible with this study  Additional exclusion criteria for participants in dose expansion (Part B3):  First-line locally advanced and/or metastatic breast cancer with no prior adjuvant chemotherapy Inflammatory breast cancer