It's unlikely to be "dominance" in a puppy. It's more likely a puppy self preservation attempt eg if they can't flee - they will fight. You put him in that situation, and if you keep doing that then yes he will be agressive because you're training him to be that way by not giving him any other choice or protecting him. If you want to understand more about what your dog is trying to tell you - I recommend Turid Rugaas book or dvd or both "Calming Signals". My dog loves watching the DVD.I can understand why he did this (dominance, tired, feeling overwhelmed)
Turid Rugaas - Calming Signals Community
Puppies are very forgiving. As long as at least 4 out of 5 times - you get the experience right and fun for the puppy, the puppy will learn what you want.
Ian Dunbar's site is called Dog Star Daily - here
Digital Dog Training Textbook | Dog Star Daily
Another site about puppy training using reward based methods and not punishment or scolding is here.
Susan Garrett Agility Training
Beware of any training advice that talks about "dominance" or "alpha rolls" like they are things you want to prevent and do. That stuff has largely been proven wrong, based on bad research and the methods are likely to get the owner bitten.
Misconceptions of the Mythical Alpha Dog | Dog Star Daily
You don't want to allow the puppy to be naughty all the time. You do want to actively encourage and reward good behaviour. But how you stop the naughty stuff is often as simple as distracting your dog and giving it something else to do and rewarding that.
Labradors are not born well behaved - in fact they are usually extremely naughty and depending how you manage them - can be aggressive. I don't know much about Pyranean Mountan Dogs but I thought they were an in-the-paddock livestock guard dog - so they are not naturally sociable - doesn't mean you can't train them to love people, but you need to do it so being with people is always a fun and pleasant experience for the dog.
If you are likely to be places where there are badly behaved people and children - you may want to invest in a fold up crate and crate train your dog to enjoy being in there. The soft sided crates in particular - stop little children's fingers from dog poking and give the dog a safe place to be.
Crate Training : The Humane Society of the United States