Is there an upper limit for SMS collection?

No, you can set "Delete old information (automatically delete old information when the information reaches the maximum number)" and find the setting menu yourself in the SMS program. Generally, "Delete old information (automatically delete old information when the information reaches the maximum number)" is checked by default, and you don't need to set it yourself. By default, old information will be automatically deleted when it reaches 200. Even if you don't check delete old information, there will be no receiving limit unless your mobile phone has no memory space.