The purpose of this study is to determine the recommended phase 2 dose (RP2D) regimen(s) of JNJ-78306358 in Part 1 (Dose Escalation) and to determine the safety of JNJ-78306358 at the RP2D regimen(s) in Part 2 (Dose Expansion).

JNJ-78306358 is a bispecific antibody binding to CD3 on T cells and human leukocyte antigen G (HLA-G) on cancer cells. The study consists of a screening phase, a treatment phase, and a post-treatment follow-up phase. Study evaluations include safety, pharmacokinetics, biomarkers, immunogenicity, and efficacy (disease evaluations). The total study duration will be up to 2 years 4 months.

Inclusion Criteria

• Histologically or cytologically confirmed, metastatic or unresectable solid tumor of one of the following types:

  a. Renal Cell Carcinoma (RCC): clear cell or papillary carcinoma, b. ovarian cancer: high grade serous epithelial ovarian; primary peritoneal or fallopian tube cancer; 1. low grade or non-serous histologies are not allowed; c. colorectal cancer (CRC); d. other tumor types (including lung adenocarcinoma, endometrial cancer, and pancreas cancer) may be enrolled with sponsor approval

• Measurable or evaluable disease: a. Part 1: either measurable or evaluable disease; b. Part 2: at least one measurable lesion per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. Participants with ovarian cancer without a measurable lesion must have disease evaluable per RECIST version1.1 (example ascites) or have Cancer antigen 125 (CA 125) greater than (>) 2*upper limit of normal (ULN) within 2 weeks prior to first dose of study drug

• Progressed during or after the following prior therapies for metastatic disease, unless participant was ineligible to receive them: a) RCC: clear cell histology: an antiangiogenic agent and an immune checkpoint inhibitor, administered as 1 or more lines of therapy. For papillary renal carcinoma 1 line of systemic therapy; b. CRC: at least 2 lines of therapy including a fluoropyrimidine, oxaliplatin, and irinotecan given with or without antiangiogenic therapies or epidermal growth factor receptor (EGFR) antibodies. In addition, prior treatment with anti-programmed cell death protein 1 (PD1) antibody is required for high microsatellite instability (MSI-H) CRC; c. ovarian cancer: at least 2 lines of therapy, including at least 1 line with platinum. Maintenance therapy after completion of platinum-containing regimen, example with bevacizumab or a poly- Adenosine di-phosphate (ADP) ribose polymerase inhibitor will not count as a separate line of therapy; d. other tumor types: at least 2 lines of systemic therapy

• Eastern Cooperative Oncology Group (ECOG) performance status grade of 0 or 1

• Selected participants in pharmacokinetics/pharmacodynamic (PK/PD) cohorts and in Part 2 must agree to undergo the mandatory tumor biopsies

Exclusion Criteria:

• Active central nervous system involvement
• Toxicity from prior anticancer therapy has not resolved to baseline levels or to Grade less than or equal to (<=) 1 (except alopecia, vitiligo, peripheral neuropathy, or endocrinopathies that are stable on hormone replacement, which may be Grade 2)
• Clinically significant pulmonary compromise
• Autoimmune or inflammatory disease requiring systemic steroids or other immunosuppressive agents (example, methotrexate or tacrolimus) within 1 year prior to first dose of study drug
• Solid organ or bone marrow transplantation

The data sharing policy of the Janssen Pharmaceutical Companies of Johnson & Johnson is available at www.janssen.com/clinical-trials/transparency. As noted on this site, requests for access to the study data can be submitted through Yale Open Data Access (YODA) Project site at yoda.yale.edu