The limitation is not set on a specific number of items/space or attractions in the park, as such. More accurately, the game is designed to show you this message when you hit the limits of what your specific device can efficiently handle before becoming more vulnerable to crashing.
We have some advice on how to avoid this happening too soon when building your park.
Firstly, it's worth ensuring that when you play RollerCoaster Tycoon 3, you've closed down any other apps that you don't need open through your iOS devices' multi-tasking menu. This can be accessed by double-tapping the home button.
Next up, some things in-game will require more power than others: For example, custom-built rollercoasters are more difficult to process than the preset ones. Waterfalls and water rides require a bit more processing than non-water-based rides, and so on.
If you require further assistance, please use the button below to raise a support ticket with us: