Hello Kelly! Thanks for bringing your question to planDisney!
Disney's Hollywood Studios is in high demand! There have been a few instances, over the past few months, when additional capacity is added to the Disney Parks after initially being marked as unavailable. When I booked a vacation for December, there wasn't availability at Disney's Hollywood Studios. Shortly before our trip, I checked again and saw that availability had been added!
While I can't guarantee that additional capacity will be added, I encourage you to check the Disney Park Pass reservation calendar daily, if not multiple times per day. That will be your best chance to see if availability is added to Disney's Hollywood Studios between now and your June visit.
In looking at the
Disney Park Pass calendar, I see park availability at
Magic Kingdom Park,
EPCOT, and
Disney's Animal Kingdom around the time of your planned visit. If you haven't already, make your reservations for those parks! June is becoming popular for visits! Also, Guests do not need a Disney Park Pass reservation to visit
Disney's Blizzard Beach Water Park. This park can be a welcome break from the theme parks during the hot summer months!
Hakuna Matata! Jonathan