This study will be conducted to assess the safety and tolerability of BOS172722 when administered as monotherapy and in combination with paclitaxel in participants with advanced nonhaematologic malignancies and also to establish the maximum tolerated dose and recommended Phase 2 dose of BOS172722 in combination with paclitaxel in those participants.

Inclusion Criteria:

Participants are eligible to be included in the study only if all of the following criteria apply:

• For Part A only, histopathologically confirmed diagnosis of an advanced nonhaematologic malignancy

• For Part B only, histopathologically confirmed diagnosis of triple-negative breast cancer

• No standard curative treatment or has declined standard therapy

• Eastern Cooperative Oncology Group performance status 0 or 1, measured within 72 hours before the first BOS172722 or paclitaxel dose

• Predicted life expectancy of ≥ 3 months

• Adequate renal function (creatinine ≤ 1.5 × upper limit of normal [ULN] or glomerular filtration rate ≥ 50 milliliters per minute [mL/min])

• Adequate hepatic function:

  • Total bilirubin ≤ 1.5 × ULN
  • Aspartate transaminase ≤ 3 × ULN (or ≤ 5 × ULN if due to liver involvement by tumor)
  • Alanine transaminase ≤ 3 × ULN (or ≤ 5 × ULN if due to liver involvement by tumor)

• Adequate bone marrow function:

  • Hemoglobin ≥ 9.0 grams per deciliter (g/dL)
  • Platelet count ≥ 100 × 10^9 cells per liter (cells/L)
  • Absolute neutrophil count ≥ 1.5 × 10^9 cells/L

• Mean corrected QT interval as calculated by the Fridericia correction formula < 470 milliseconds

• Willingness to use adequate contraceptive methods

• Capable of giving signed informed consent

• Willingness to avoid direct sunlight and the use of tanning equipment during the study and for at least 30 days after the last BOS172722 dose

Exclusion Criteria:

Participants are excluded from the study if any of the following criteria apply:

• For Part A combination cohorts and Part B: a history of hypersensitivity to paclitaxel
• Persistent clinically significant toxicity from prior chemotherapy > Grade 1, excluding alopecia
• Unable to swallow oral capsules
• Gastrointestinal (GI) condition which could interfere significantly with the absorption of study medication
• History of upper GI bleeding, ulceration, or perforation within 6 months before the first or paclitaxel BOS172722 dose
• Uncontrolled or severe concurrent medical condition (including uncontrolled brain metastases). (Stable brain metastases either treated or being treated with a stable dose of steroids/anticonvulsants, with no dose change within 28 days before the first BOS172722 or paclitaxel dose, will be allowed.)
• History of stroke or cerebrovascular accident within 3 months before the first BOS172722 or paclitaxel dose
• Any evidence of serious active infection
• Uncontrolled or severe cardiovascular disease, including myocardial infarct or unstable angina within 6 months before the first BOS172722 or paclitaxel dose, New York Heart Association Class II or greater congestive heart failure, serious arrhythmias requiring medication for treatment, clinically significant pericardial disease, or cardiac amyloidosis
• Uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements
• Known infection with Human Immunodeficiency Virus or hepatitis A, B, or C (testing not required)
• Major surgery within 28 days before the first BOS172722 or paclitaxel dose
• Pregnant or breastfeeding
• Active treatment for a secondary malignancy
• Cancer-directed therapy (chemo-, radio-, immuno-, biologic, or hormonal therapy with the exception of luteinizing hormone-releasing hormone agonists/antagonists, receptor activator of nuclear factor kappa-B ligand inhibitors, and bisphosphonates) within 21 days or 5 half-lives, whichever is longer, before the first BOS172722 or paclitaxel dose (Palliative radiotherapy is allowed before initiating study treatment if any associated toxicity resolved to ≤ Grade 1.)
• Use of a medication known to be a strong or moderate inhibitor or inducer of CYP3A4 within 14 days before the first BOS172722 or paclitaxel dose
• Use of a medication known to be a substrate of CYP3A4 and to have a narrow therapeutic range within 14 days before the first BOS172722 or paclitaxel dose
• Consumption of grapefruit or Seville oranges (including juice, marmalade, etc.) within 14 days before the first BOS172722 or paclitaxel dose