Instead of sharing suggestions whenever they come to mind, consider writing them down, so you can share them in batches. By giving them time to coalesce, you can be more thoughtful in advocating for the ones you feel more strongly about and figuring out whether any of them are trying to solve the same underlying problem. Not only is it more polite, but it also makes you seem organized and efficient, since you can rattle off your ideas in quick succession.
This is also more considerate of everyone's head space, since it takes time to context switch from what they were doing to listen to your suggestions. As a result, you're more likely to get someone's undivided attention, which means that you'll end up being able to make more suggestions in aggregate than if you were to offer them one-by-one.