Study to Evaluate Adverse Events, Change in Disease Activity, and How ABBV-706 Moves Through the Body When Intravenously (IV) Infused Alone or in Combination With IV Infused Budigalimab, Cisplatin, or Carboplatin in Adult Participants With Advanced Solid Tumors

* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * The laboratory values criteria must be met within 7 days prior to the first dose of study drug as per the protocol. * QT interval corrected for heart rate (QTc) \<= 450 msec (males) or \<= 470 msec (females) using Fridericia's correction, and an ejection fraction of \>= 50% as measured by echocardiogram or multigated acquisition (MUGA) scan at Screening. * Part 1 only: Advanced recurrent or refractory solid tumors with potential SEZ6 expression including small cell lung cancer (SCLC), high-grade central nervous system (CNS) tumors (glioblastoma \[GBM\], IDH-wildtype Grade 4; oligodendroglioma, IDH-mutant, and 1p/19q-codeleted Grade 3; astrocytoma, IDH-mutant Grade 3 or Grade 4), neuroendocrine prostate cancer (NEPC), high-grade poorly differentiated gastroenteropancreatic neuroendocrine carcinoma (GEP-NEC)s, large cell neuroendocrine carcinoma (LCNEC)s, SCLC transformed from epidermal growth factor receptor (EGFR) mutant non-small cell lung cancer (NSCLC), atypical lung carcinoids, and other high-grade poorly differentiated NECs, who have progressed on or after standard of care (SoC) therapy and with no curative therapy available. For SCLC, participants must have histologically or cytologically confirmed SCLC that is relapsed or refractory following at least 1 prior platinum-containing chemotherapy. * Part 2 only: Histologically or cytologically confirmed SCLC that is relapsed or refractory (R/R) following at least 1 prior platinum-containing chemotherapy and with no curative therapy available. For the purposes of this study, a line of therapy is defined as \>= 1 complete cycle of either a single agent or combination of drugs, including any planned sequential therapy of various regimens. * Part 3a only: SCLC or Grade 3 NETs and poorly differentiated NECs. Specific tumor types include but not limited to NEPC, GEP-NECs, LCNECs, SCLC transformed from EGFR mutant NSCLC, MTC, and other NECs (atypical lung carcinoids that have received prior chemotherapy are allowed) * Part 3b only: SCLC who have only progressed following a frontline regimen containing a platinum-based chemotherapy (i.e., second-line SCLC subjects) or Grade 3 NETs and poorly differentiated NECs. Specific tumor types include but not limited to NEPC, GEP-NECs, LCNECs, SCLC transformed from EGFR mutant NSCLC, MTC, and other NECs (atypical lung carcinoids that have received prior chemotherapy are allowed)tumors (GBM, IDH-wildtype Grade 4; oligodendroglioma, IDH-mutant, and 1p/19q-codeleted Grade 3; astrocytoma, IDH-mutant Grade 3 or Grade 4) who have progressed on SoC therapy and with no curative therapy options available. * Part 4b only: Grade 3 NETs and poorly differentiated NECs. Specific tumor types include but not limited to NEPC, GEP-NECs, LCNECs, SCLC transformed from EGFR mutant NSCLC, MTC, and other NECs (atypical lung carcinoids that have received prior chemotherapy are allowed) * Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 for participants with extracranial solid tumors or Response Assessment for Neuro-Oncology (RANO)for participants with primary high-grade CNS tumors (GBM, IDH-wildtype Grade 4; oligodendroglioma, IDH-mutant, and 1p/19q-codeleted Grade 3; astrocytoma, IDH-mutant Grade 3 or Grade 4). * Primary CNS tumors within 12 weeks from radiation therapy should have unequivocal progression as documented by either tumor recurrence predominantly outside of radiation field on magnetic resonance imaging (MRI) or confirmed on tumor biopsy. * Participants with brain metastases from an extracranial solid tumor are eligible if the brain metastases as outlined in the protocol. * Fresh or archival tumor tissue available for submission, for retrospective SEZ6 expression analysis as outlined in the protocol.

* History of interstitial lung disease (ILD) or pneumonitis that required treatment with systemic steroids, nor any evidence of active ILD or pneumonitis. * History of idiopathic pulmonary fibrosis or organizing pneumonia. * Prior treatment with an antibody drug conjugate that consists of a Top1 inhibitor payload. * Part 2 only: Prior treatment with a SEZ6-targeted antibody drug conjugate.