I think Larry_H_10's comment above is good, balanced and pragmatic. I'm a lifelong stutterer and saw my cousin grow out of it around school age, while I did not. There's a lot of different factors, but I like his suggestion to reduce demands, especially when this young. I'm of the opinion that intensive speech therapy at this age is detrimental, so I would look into studies on that if you're considering it. One question, are you sure it's stuttering? You mentioned that he repeats words 10+ times, seemingly involuntarily to the point of covering his mouth. I can see this being stuttering in the right context (like he's trying to get through the following word, or there's obvious struggle to physically say the word), but I was just wondering if you considered this.