A Study of MK-8109 (Vintafolide) Given Alone or With Chemotherapy in Participants With Advanced Cancers (MK-8109-001)

Inclusion criteria for all participants:

* Histologically-confirmed metastatic or locally advanced solid tumor that has failed to respond to standard therapy, progressed despite standard therapy, or for which standard therapy does not exist or is unacceptable to the participant
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* At least one measurable metastatic or recurrent lesion
* No history of a previous malignancy with the exception of cervical intraepithelial neoplasia, basal cell carcinoma of the skin, or adequately treated localized prostate carcinoma; or has undergone potentially curative therapy with no evidence of disease for five years
* Adequate organ function
* Female participants of childbearing potential must be willing to use acceptable methods of birth control or abstain from heterosexual activity for the course of the study through 90 days after the last dose of study therapy
* Male participants must agree to use an adequate method of contraception for heterosexual activity starting with the first dose of study therapy through 90 days after the last dose of study therapy

Inclusion criteria for Part A:

* Tumor lesions characterized as folate receptor (FR) 100% as determined by an etarfolide Sequential Single Photon Emission Computed Tomography (SPECT) and CT scan
* Histologically-confirmed diagnosis of locally advanced or metastatic or recurrent endometrial cancer

Inclusion criteria for Parts B \& C:

\- Must have an etarfolatide SPECT/CT scan to determine FR status

Exclusion criteria for all participants:

* Part A \& Part C if enrolled after completion of Part B: Chemotherapy, radiotherapy, or biological therapy (including monoclonal antibodies) within 4 weeks prior to drug administration, or not recovered from adverse events due to agents administered more than 4 weeks earlier
* Part B: Chemotherapy, radiotherapy, or biological therapy (including monoclonal antibodies) within 3 weeks prior to drug administration, or not recovered from adverse events due to agents administered more than 4 weeks earlier
* Currently participating or has participated in a study with an investigational compound or device within 28 days of initial dosing on this study
* Part A, dose escalation, Parts B and C: More than 3 prior cytotoxic regimens for metastatic disease.
* Part A, dose confirmation: Has received more than 2 prior cytotoxic regimens for metastatic disease.
* Primary central nervous system (CNS) tumor
* Active CNS metastases and/or carcinomatous meningitis.
* Known hypersensitivity to the components of the study therapy or its analogs
* Recent (i.e., ≤ 6 weeks) history of abdominal surgery or peritonitis
* Bowel occlusion or sub-occlusion
* Prior whole abdominal or whole pelvis radiation therapy or radiation therapy to \>10% of the bone marrow at any time in the past or prior radiation therapy within the last 3 years to the breast / sternum, head, or neck
* Requires anti-folate therapy for the management of co-morbid conditions
* Known regular user (including "recreational use") of any illicit drugs or had a recent history (within the last year) of drug or alcohol abuse
* Pregnant or breastfeeding or expecting to conceive, or donate sperm within the span of the study
* Human Immunodeficiency Virus (HIV)-positive
* Active Hepatitis B or C
* Symptomatic ascites or pleural effusion.
* History of stem cell or bone marrow transplant

Exclusion Criteria for Part B:

* Permanent pacemaker
* Unable to refrain from use of all concomitant medications on Day 1
* Structural heart disease, history of myocardial infarction (MI), or unstable angina
* History of cardiac arrhythmia, congestive heart failure (CHF), sick sinus syndrome, second or third degree atrioventricular (AV) block
* History of risk factors for Torsades de Pointes such as CHF, uncorrected hypokalemia, family history of long QT syndrome