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