Inclusion Criteria:

          -  Has a histologic or cytologic diagnosis of a malignant solid tumor.

          -  Participants enrolled in Part 2a (monotherapy, dose expansion) must have small cell
             lung cancer (SCLC) with tumors that express B7H3 above a given threshold per central
             laboratory testing; participants enrolled to Part 2b (combination therapy, dose
             expansion) must have either NSCLC or HR-positive/HER2-negative breast cancer with
             tumors that express B7H3 above a given threshold per central laboratory testing.

          -  Measurable disease defined by Response Evaluation Criteria in Solid Tumors (RECIST)
             criteria.

          -  An Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to
             2.

          -  Failure of at least 1 prior systemic chemotherapy including all available standard
             therapies for participants in the dose-escalation phase (Parts 1a and 1b).

          -  All participants with breast cancer for subjects in the dose-expansion phase (Part 2b
             only) must have the following:

          -  locally advanced or metastatic HR-positive/HER2-negative breast cancer after failing
             cyclin-dependent kinase (CDK)4/6 inhibitor-based therapy.

          -  HR-positivity and HER-2-negativity should be confirmed based on American Society of
             Clinical Oncology (ASCO)/College of American Pathologists (CAP) criteria.

          -  All participants with non-small cell lung cancer (NSCLC) for participants in the
             dose-expansion phase (Part 2b only) must have R/R NSCLC after at least 1 line of
             therapy.

          -  All participants with SCLC in the dose-expansion phase (Part 2a only) must have R/R
             SCLC from at least 1 line of therapy which includes a platinum-based therapy with or
             without an anti-PD-1/PD-L1 therapy.

          -  All participants with either breast cancer or NSCLC must have the following if exposed
             to prior taxane-based therapy: no history of taxane allergy (Part 1b and Part 2b
             only); and disease that has relapsed or progressed at least 2 months after most recent
             exposure to any taxane-based therapy.

          -  Available tumor tissue suitable for immunohistochemistry testing.

          -  Adequate kidney, liver, and hematologic laboratory values as described in the
             protocol.

        Exclusion Criteria:

          -  Untreated brain or meningeal metastases (participants with a history of metastases may
             be eligible based on details described in the protocol).

          -  Grade 2 or higher peripheral neuropathy (only applies to participants who would
             receive taxane therapy).

          -  Unresolved Grade 2 or higher toxicities related to previous anticancer therapy except
             alopecia.

          -  Known active infection of hepatitis B, hepatitis C, or human immunodeficiency virus
             with exceptions as described in the protocol.

          -  Recent history (within 6 months) of congestive heart failure (defined in the
             protocol), ischemic cardiovascular event, cardiac arrhythmia requiring pharmacological
             or surgical intervention, pericardial effusion, or pericarditis.

          -  Any history of hypersensitivity to any ingredients of ABBV-155 will be excluded. For
             combination therapy only (Parts 1b and 2b), no history of serious allergic reaction to
             any taxane or any ingredients used in taxane formulation (e.g., cremaphor).