Bringing a new puppy into the family with a Skye Terrier can be a trying time for all. It is important to remember that the reactions of your Skye to the new puppy may be much more involved than you realize. You should protect the new puppy from potential harm from the Skye but you need to allow them to establish a natural order for doing things as well.
Dogs in general but Skyes in particular are pack animals and need the structure of a pack in order to know their places and be happy. Whenever a new person or animal is brought into the pack there are going to be moments when your Skye is going to make his bid for dominance in the pecking order. You need to have rules and enforce the rules but you also need to allow the new puppy to learn its place in the hierarchy as well as your Skye.
You want to make a point of never leaving the new puppy and Skye together unsupervised and you want to watch carefully as they interact. Chances are your Skye will eventually grow resigned, at the very least, to the fact that the new puppy is there to stay and either learn to incorporate the new puppy into the pack or work studiously to disregard the new puppy all together.
Adding another puppy to the mix may sound like an enticing prospect, especially as your Skye ages and loses some of the puppy qualities that many puppy owners really love. You need to think carefully about what it means to own two puppies before making the decision especially when one of those puppies is a Skye Terrier. Skyes are not very sociable by nature and will feel threatened by the new puppy to some degree. There will be struggles among the puppies and a little bit of 'acting out' on behalf of your Skye. You need to nip the acting out in the bud or it could prove to be very problematic later on.
You should also consider having both dogs neutered to diminish some of their more aggressive tendencies before they have the opportunity to become a problem. Of course, this won't eliminate them all together but may help make them a little less destructive. Not only is it likely that the two puppies will fight on occasion, especially as they age but also that they will vie for your affection and attention. Unfortunately this is sometimes accomplished, especially on the part of Skyes by being destructive.
Ultimately, you will want to introduce your Skye to a new puppy very carefully if at all. General recommendations are not to have more than one puppy but that simply doesn't work for some families and some breeds. If you are going to have two puppies with a Skye Terrier it is best to bring them up together from puppies rather than introducing a new puppy to the pack when your Skye is older.