This study is to evaluate the tolerability and safety of ONO-7428 in participants with unresectable advanced or recurrent solid tumors.

Inclusion Criteria:

1. Participants with histologically or cytologically confirmed unresectable advanced or recurrent solid tumors.

   [Backfill cohort only] Participants with histologically or cytologically confirmed Stage IIIB, IIIC, IV, or recurrent NSCLC according to UICC-TNM classification.

2. Participants who are refractory or intolerant to standard therapy.

3. Participants with a tumor type for which anti-PD-(L)1 antibodies have been approved and who have previously treated with anti-PD-(L)1 antibody containing regimen.

4. Participants with Eastern Cooperative Oncology Group Performance Status 0 or 1.

5. Participants with tumor tissue samples available for biomarker testing.

Exclusion Criteria:

1. Participants with a complication or history of severe hypersensitivity to any other antibody drugs.
2. Participants with concurrent autoimmune disease or a history of chronic or recurrent autoimmune disease
3. Participants with severe peritoneal dissemination.
4. Participants with pericardial fluid, pleural effusion, or ascites requiring treatment.
5. Participants with uncontrolled tumor-related pain.
6. Participants with active or history of interstitial lung disease or pulmonary fibrosis.