If you have a clear vision for yourself as a student, plus the presentation materials to show that you can manage to reach your vision within given time and circumstances, you will have a good chance to succeed. Especially for programs having an overlap with ID, and I’d say interior design has a 50-60% overlap in skills and work process, it will be possible to make the transfer. If the mindset of a designer is there already, you will have to work extra hard to master the new skills and theoretical background, but it will make it possible.