This is a non-randomized two-part study of MK-4827 given with temozolomide in participants with advanced cancer. In Part A of the study, the dose-limiting toxicities (DLTs) and the maximum tolerated dose (MTD) of MK-4827 when combined with temozolomide will be found by increasing the MK-4827 dose level in successive cohorts. In Part B of the study, participants with advanced glioblastoma multiforme and advanced melanoma will be enrolled to further evaluate the tolerability and efficacy of the MK-4827 + temozolomide combination.

Inclusion criteria

Part A

• Participants with histologically-confirmed advanced solid tumors who have failed to respond to standard therapy, or progressed on standard therapy, or for whom standard therapy does not exist.

Part B

• Participants must have a histologically-confirmed recurrent glioblastoma multiforme (GBM) with radiographic evidence of progression/recurrence of disease, with up to two prior treatment regimens (not including temozolomide or bevacizumab) for their recurrent disease.

OR

• Participants must have histologically-confirmed recurrent or metastatic melanoma for which the participant has received up to two prior therapies.
• Participants must not have received prior treatment with cytotoxic chemotherapy including temozolomide, dacarbazine, or PARP inhibitors.

Part A and Part B

• Participants with Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1.
• Participants must have adequate organ function.
• Women of childbearing potential and male participants must agree to use an adequate method of contraception starting with the first dose of study drug through 90 days after the last dose of study drugs.
• Participant has no history of a prior malignancy with the exception of gliomas (as secondary GBM is allowed), cervical intraepithelial neoplasia, basal cell carcinoma of the skin, or adequately treated localized prostate carcinoma with Prostate-Specific Antigen (PSA) < 1.0; or who has undergone potentially curative therapy with no evidence of that disease for five years, or who is deemed at low risk for recurrence by his/her treating physician.
• Participant has at least one measurable metastatic or recurrent lesion.

Exclusion criteria

• Participant has had chemotherapy, radiotherapy, or biological therapy within four weeks prior to study Day 1 (six weeks for nitrosoureas and mitomycin C) or who has not recovered from adverse events due to agents administered more than four weeks earlier.
• Participants with known symptomatic or progressive Central Nervous System (CNS) metastases and/or carcinomatous meningitis.
• Participant has prior exposure to PARP inhibitors. Prior exposure to temozolomide is allowed only for participants with GBM, provided it was received in the adjuvant setting with GBM progression after completion of adjuvant temozolomide treatment and a treatment-free interval of ≥ 3 months.
• Participant has significant or uncontrolled cardiovascular disease, including New York Heart Association (NYHA) Class III-IV heart failure, unstable angina, or a myocardial infarction within the last six months.
• Participant is breastfeeding.
• Participant is known to be Human Immunodeficiency Virus (HIV)-positive.
• Participant has active Hepatitis B or C.
• Participant has symptomatic ascites or pleural effusion.
• Participant has a requirement for concurrent treatment with immunosuppressive agents.
• Participant must not have prior radiation therapy to more than 30% of hte bone marrow and must have recovered for at least 3 weeks from the hematologic toxicity of prior radiotherapy.
• Participant has had a prior stem cell or bone marrow transplant.