I would say it’s possible. Here at the seminary where I am, we have several such cases. Our rector actually comes from my diocese, but he has been ordained in the diocese of Providence. A seminarian here is from Delaware, but is studying for Providence. Another is from my diocese, but is studying for the diocese of Burlington. However, each usually has some link to the diocese for which they intend to serve. The rector may have grown up in the town right next to me, but he lived for a few years in Rhode Island, and loved it enough to be ordained there. The guy who wishes to be a priest in Vermont went there to college for a few years, so he wishes to become a priest there. I know of a seminarian who apparently decided to serve in another diocese because the one he grew up in was too urban, and he preferred the small town life.
However, I think that not every diocese will always decide to do it. Some may think your reasons for trying to join their diocese are questionable. It really depends on their vocation director or bishop. However, given the current lack of vocations, it might not be hard. I do recommend that you deeply think about switching to another diocese. It’s a big decision, because this determines where you live for the rest of your life. After ordination, it’s hard to switch. So be sure.
Also, always consider whether or not you’re called to become a religious priest, in which case you probably won’t be in service to a diocese, but to an order or a congregation. There, you’d have more mobility. However, do not allow simply join an order to be allowed to move around. Vocation isn’t something to be taken lightly.
