This study is one single group of participants with non-small cell lung cancer (NSCLC) who have not been cured by other treatments. It is the first time the drug has been used in humans. There will be two parts and a sub-study. The primary purpose of the parts are: * Dose Escalation: To investigate the safety and tolerability and to determine the maximum tolerated dose (MTD) and the recommended dose for expansion (RDE) of DS-1062a * Dose Expansion: To investigate the safety and tolerability of DS-1062a in additional solid tumors This study is expected to last approximately 6 years from the time the first participant is enrolled to the time the last subject is off the study. Study sites are located in both the United States and Japan. The number of treatment cycles is not fixed in this study. Participants who continue to benefit from the study treatment may continue, unless: * they withdraw * their disease gets worse * they experience unacceptable side effects. The primary purpose of the sub-study is to compare the effectiveness of steroid versus non-steroid mouthwash as prophylaxis against oral mucositis/stomatitis in participants receiving DS-1062a. The sub-study is a randomized study that will include approximately 76 participants enrolling into the Dose Expansion part.
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Number of participants with dose-limiting toxicities
Timeframe: Within 8 cycles (each cycle is 21 days)
Number of participants with adverse events (AEs)
Timeframe: When all participants have either discontinued the study or the last participant enrolled in the study has completed at least 6 months of follow up (approximately 4 years)
Number of participants with Grade >/= 2 oral mucositis/stomatitis in Sub-Study
Timeframe: At 8 weeks