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) diagnosis; participants enrolled to Part 2b (combination therapy, dose expansion) must have either NSCLC or HR-positive/HER2-negative breast cancer.
* 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) including the safety lead-in phase (Japan only).
* 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. Participants with activating mutations in EGFR, ALK/ROS1, BRAF genes, or with positive expression of PD-L1 must have been treated with the appropriate targeted therapies.
* 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).
* 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).
