This is a four-part dose-escalation and confirmation study in participants with advanced solid tumors. Part A is for dose escalation and determination of maximum tolerated dose (MTD) and recommended Phase 2 dose (RP2D) of MK-4827. Part B is a prostate/ovarian cancer cohort expansion. Part C is for a cohort of participants with relapsed or refractory T-cell prolymphocytic leukemia (T-PLL) or chronic lymphocytic leukemia (CLL). Part D will be for a cohort of participants with locally advanced or metastatic colorectal carcinoma (CRC), persistent or recurrent endometrial carcinoma, locally advanced or metastatic triple negative or highly proliferative estrogen receptor positive (ER+) breast cancer, or partially platinum-sensitive epithelial ovarian cancer. The study is also designed to find out whether MK-4827 causes at least 50% inhibition of poly adenosine diphosphate ribose polymerase (PARP) enzyme activity.

Inclusion criteria:

• For Part A, participants must have a cytologically- or histologically-confirmed metastatic or locally advanced solid tumor for which standard therapy does not exist or the participants have refused standard therapy.
• For Part B, participants must have a cytologically- or histologically-confirmed locally advanced or metastatic prostate cancer for which standard therapy does not exist or the participants have refused standard therapy or sporadic (not known to have BRCA1 or BRCA2 gene mutations) recurrent platinum resistant high grade serous ovarian, primary peritoneal, or fallopian tube cancer. Participants who progressed while receiving a platinum-containing regimen are not eligible. Participants with ovarian cancer must have at least one measurable lesion (at least 15 mm in one dimension) or a cancer antigen (CA)-125 value twice the institutional upper limit of normal (ULN).
• For Part B, participants must have archival tumor tissue available.
• For Part C, participants must have a cytologically- or histologically-confirmed diagnosis of T-PLL or B-cell CLL. Participants with T- PLL must have progressed after receiving alemtuzumab. Participants with CLL must have been refractory to or progressed within 12 months following a fludarabine-containing regimen or have received at least 2 prior therapies (before or after the fludarabine containing regimen).
• For Part D, participants must have:
• a cytologically- or histologically-confirmed metastatic or locally advanced adenocarcinoma of the colon or rectum (mCRC) and evidence of phosphate and tensin homolog (PTEN) deficiency. Participants must have received at least 1 prior 5-fluoruracil (5-FU)-based combination chemotherapy regimen for mCRC, containing oxaliplatin or irinotecan. Participants must have measurable disease.
• a cytologically- or histologically-confirmed persistent or recurrent endometrial carcinoma and measurable disease. Participants may not have had more than 1 prior chemotherapy regimen.
• a cytologically- or histologically-confirmed metastatic or locally advanced sporadic (not known to have a germline BRCA1 or BRCA2 mutation) partially platinum-sensitive recurrent epithelial ovarian cancer, fallopian tube cancer or primary peritoneal cancer. Participants who cannot receive platinum due to allergy or toxicity are eligible. Participants with ovarian cancer may have received non-platinum containing chemotherapy between their last platinum-containing regimen and enrolling in this study. Participants must have measurable disease or an elevated CA-125 (at least 2 times the institutional upper limit of normal).
• a cytologically- or histologically-confirmed metastatic or locally advanced carcinoma of the breast that either lacks expression of the estrogen receptor (ER), progesterone receptor (PR) and HER2 (triple negative [TN]) or is ER and/or PR+ . Participants with locally advanced disease must have recurrent or progressive disease that is not suitable for treatment with curative intent. Participants with ER positive disease must have been treated with at least one line of hormonal therapy for recurrent/progressive disease or have been on hormonal therapy at the time of recurrence/progression. Participants with either ER+ or TN tumors may not have had more than 1 line of chemotherapy for treatment of recurrent disease. If participants received adjuvant chemotherapy they must have had a disease-free interval of at least 6 months from the completion of adjuvant chemotherapy. Participants must have measurable disease.
• Participant must have performance status ≤2 on the ECOG Performance Scale.
• Participant must have adequate organ function.
• Female participants of childbearing potential must have a negative pregnancy test within 72 hours prior to receiving the first dose of study medication.
• Participants with prostate cancer must continue on luteinizing-hormone-releasing hormone (LHRH) analogues if they have not had an orchiectomy to achieve a sustained baseline serum testosterone < 50 ng/dL.

Exclusion criteria:

• Participant who has had chemotherapy, radiotherapy, hormonal or biological therapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to first dose of study drug.
• Participant is currently participating or has participated in a study within 30 days or 5 half lives (which ever is longer) of administration of an investigational agent or within 30 days of participating in a study using an investigational device.
• Participants who have received bevacizumab may enter the trial 4 weeks after their last dose of bevacizumab if all bevacizumab-related toxicities have resolved.
• Participant with a history of a prior malignancy with the exception of cervical intraepithelial neoplasia; basal cell carcinoma of the skin; adequately treated localized prostate carcinoma with prostatic-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.
• Participants with known central nervous system (CNS) metastases and/or carcinomatous meningitis are excluded.
• Participant with a known primary central nervous system tumor.
• Participant has known hypersensitivity to the components of study drug or its analogs.
• Participant has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
• Participant is, at the time of signing informed consent, a regular user (including "recreational use") of any illicit drugs or had a recent history (within the last year) of drug or alcohol abuse.
• Participant is pregnant or breast feeding, or expecting to conceive or father children within the projected duration of the study.
• Participant is known to be Human Immunodeficiency Virus (HIV)-positive.
• Participant has known history of Hepatitis B or C.
• Participant has symptomatic ascites or a symptomatic pleural effusion.
• Participant has participated in a clinical trial with a known or putative PARP inhibitor.
• Participants with T-PLL or CLL with active autoimmune hemolytic anemia.
• Participants may not have had therapy with corticosteroids at greater than or equal to 20 mg/day prednisone equivalent within 2 weeks prior to the first dose of treatment.