This is a phase 1 study to test different doses of a new investigational drug called CFI-400945 to see which dose is safer in people. This study will also look at the safety of CFI-400945 and to study its effects on patients with advanced cancers. This drug has been tested in animals but not yet in people.

CFI-400945 is an oral (taken by mouth) drug that works by blocking polo-like kinase 4 (PLK4) from working. PLK4 is a protein that is important in regulating cell growth and division and cell death. Many tumors are shown to make too much PLK4. When there is too much PLK4 produced, it is believed to lead to uncontrolled cancer cell growth and division. Therefore, by blocking this protein from working, it is believed to stop tumors growing or shrink them.

All participants will receive CFI-400945. At the beginning of the study, participants are given a low dose of CFI-400945 and are watched very closely to see what side effects they have and to make sure the side effects are not severe. If the side effects are not severe, then more participants are asked to join the study and are given a higher dose of study drug. Participants joining the study later on will get higher doses of study drug than participants who join earlier. This will continue until the highest dose of study drug that can be taken without severe side effects is found (called maximum tolerated dose). Doses higher than that will not be given.

After the best dose of study drug is found, additional participants will be asked to join the study and will be given the study drug at the maximum tolerated dose to further test the safety and the drug at that dose.

Inclusion Criteria:

• Have histologic or cytological proof of advanced cancer that has progressed and for which there is no further standard anticancer therapy available in the opinion of the investigator.
• Patients must have measurable disease as per RECIST v1.1
• Are 18 years of age or older.
• Have clinically acceptable laboratory screening results within certain limits
• Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
• Able to swallow oral medications.
• Have a life expectancy greater than 3 months.
• Women and men of child producing potential must agree to use highly effective means of contraception during study participation, and for at least 30 days after the last administration of study medication.
• Negative serum pregnancy test with 72 hours prior to start of study drug
• Have the ability to understand the requirements of the study, provide written informed consent which includes authorization for release of protected health information, abide by the study restrictions, and agree to return for the required assessments.

Exclusion Criteria:

• Women who are pregnant or nursing.
• Have received radiotherapy, chemotherapy, biological therapy or investigational treatment less than four weeks (six weeks for nitrosourea or mitomycin C) prior to first dose of study medication or have not recovered from all acute toxicities from prior treatments.
• Patients who have received growth factors within 14 days prior to initiation of dosing of CFI-400945 fumarate.
• Have active, acute, or chronic clinically significant infections.
• Have uncontrolled severe hypertension
• Have clinical symptomatic congestive heart failure defined at >= Class II of the New York Heart Association functional classification system or LVEF < 50% at baseline.
• Have active angina pectoris or recent myocardial infarction (within 6 months).
• Have chronic atrial fibrillation or QTc of greater than 470 msec, as calculated by Bazett's correction formula.
• Have had major surgery within 21 days of starting therapy. Placement of a venous access device within 21 days of starting therapy is allowed.
• Have additional uncontrolled serious medical or psychiatric illness.
• Have any medical condition that could impair the administration of oral agents including significant bowel resection, inflammatory bowel disease or uncontrolled nausea or vomiting.
• Known central nervous system metastasis. Patients with history of central nervous system metastases are eligible if they are clinically or radiographically stable for at least 3 months and not taking steroids or anticonvulsants.
• Patients being treated with full dose warfarin are excluded. Patients with history of deep vein thrombosis or pulmonary embolus who are being treated with therapeutic doses of low molecular weight heparin or prophylactic dose anticoagulants may be enrolled.
• Patients being treated with certain drugs not acceptable while receiving CFI-400945 fumarate.