The purpose of this study is to determine the putative recommended phase 2 dose(s) (RP2Ds) and best way to take (optimal route of administration) JNJ-89402638 and to determine the safety of JNJ-89402638 at the RP2D(s) in participants with metastatic colorectal cancer (mCRC) and metastatic gastric cancer (mGAC) and to determine the safety and tolerability of JNJ-89402638 in combination with bevacizumab or biosimilar with or without chemotherapy in participants with mCRC.

Inclusion Criteria:

• For Part 1 (dose escalation), Part 2 (Arm A [JNJ-89402638 monotherapy]): Have histologically or cytologically confirmed diagnosis of colorectal adenocarcinoma (CRC) progressing after 2 or more prior lines of standard therapy in the metastatic/unresectable setting; For Part 2 Arm B (JNJ-89402638 + bevacizumab or biosimilar): Have histologically or cytologically confirmed diagnosis of CRC progressing after 2 or more prior lines of standard therapy in the metastatic/unresectable setting; For Part 2 Arm C (JNJ-89402638 + FOLFOX/bevacizumab or biosimilar): Have histologically or cytologically confirmed diagnosis of microsatellite stable (MSS) or proficient mismatch repair (pMMR) CRC progressing after 1 or more prior lines of standard therapy in the metastatic/unresectable setting. Participants must have previously received a fluoropyrimidine and irinotecan doublet (such as FOLFIRI); For Part 2 Arm D (JNJ-89402638 + FOLFIRI/bevacizumab or biosimilar): Have histologically or cytologically confirmed diagnosis of MSS or pMMR CRC progressing after 1 prior line of standard therapy in the metastatic/unresectable setting. Must not have received irinotecan previously for metastatic disease; For Part 2 Arm E (JNJ-89402638 monotherapy in mGAC): Have histologically or cytologically confirmed diagnosis of gastric adenocarcinoma or gastroesophageal junction adenocarcinoma progressing after 1 or more prior lines of standard therapy in the metastatic/unresectable setting

• Have evaluable or measurable disease per response evaluation criteria in solid tumors (RECIST) version 1.1

  1. Part 1: Must have either measurable or evaluable disease
  2. Part 2: Must have at least 1 measurable lesion

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

• Have an estimated or measured glomerular filtration rate (GFR) greater than or equal to (>=) 30 milliliter per minute (mL/min) based on modification of diet in renal disease (MDRD) 4-variable formula

Exclusion Criteria:

• Active (new or progressive) brain metastases, leptomeningeal disease, or untreated spinal cord compression
• Toxicity from prior anticancer therapy that has not resolved to Grade less than or equal to (<=)1 (except alopecia, vitiligo, Grade <= 2 peripheral neuropathy, or endocrinopathies that are stable on hormone replacement). For Part 2 Arm C: Grade 2 or higher peripheral neuropathy is considered exclusionary
• Has a prior or concurrent second malignancy (other than the disease under study) unless natural history or treatment is unlikely to interfere with any study endpoints of safety or the efficacy of the study treatment
• Received glucocorticoids (doses >10 mg/day prednisone or equivalent) within 7 days prior to the first dose of study drug
• Received or plans to receive any live, attenuated vaccine within 4 weeks before the first dose of study treatment or within 4 weeks after the last dose of study treatment

The data sharing policy of Johnson & Johnson Innovative Medicine is available at www.innovativemedicine.jnj.com/our-innovation/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.