It's generally not recommended to raise multiple puppies of the same age in the same household, you can research "littermate syndrome" to learn more about the potential problems associated with it, even though your dogs aren't littermates. With 4 puppies of the same relative age, you will be spending a massive amount of time trying to provide adequate physical and mental stimulation to each individually, which is of great importance in cases where multiple pups are being raised together.
There is a definite possibility that the smaller pups could be injured by the larger pups, either unintentionally while playing/roughhousing; or as they mature and try to sort out the pecking order among themselves. Keep in mind as they mature that 3 males even without a female are unlikely to get along 100% of the time, and that a fight between either of the larger dogs and a smaller dog is likely to end in severe or possibly fatal injuries to the smaller dog. Given the increased potential for dog aggression in bull breeds, it's also possible that you could have problems between the pit bull and the others when she is grown, even though she is the only female. To reduce the risk of a serious fight, the two larger pups (and still when they are grown dogs) should always be kept separately from each other and the smaller dogs when unsupervised, which will mean at least 3 separate "groups" of dogs when they are alone, start planning how you will manage that now.
I would absolutely spay the female dog prior to her first heat (probably around 6, maybe 7 months old), as it's a distinct possibility that the 3 males will fight when she goes in heat, or with that many dogs and people, someone will slip up and you will wind up with an accidental litter. It may not be ideal to spay her prior to full physical maturation, but it's also not ideal to have 4 adolescent dogs at the same time, so you have to minimize risk of conflict where you can. I know of 2 different small dogs (one chi, one dachshund) who suffered broken jaws (among other injuries, but because of the size difference, their whole head was in the larger dog's mouth) when they got into fights with much larger male housemates over a female housemate who was in heat. Alternatively, if you must wait to spay her, you could potentially board her or house her elsewhere for the duration of her heat, but I would forgo the added expense and risk and just spay her on the "early" side.
Honestly, it would probably be best to not get the Pyr, and concentrate on the puppies you already have. Once they're grown, if you want to add another dog, you'll be in a better position to known what to expect and dedicate the time, though there's always a risk of conflict in multi dog homes.