Will a Uni ever reconsider an application?

Basically, I received a rejection from the uni I really wanted to go to today. I'm currently at another uni and I'm hoping to transfer to a new uni as I'm not enjoying it here. When I asked for feedback they said it was due to my predicted grades - I've recently discovered my referee failed to mention a predicted grade for my current degree program. I was wondering if they would be willing to reconsider my application if I'm able to get my referee to provide them with this information?

Has anyone ever been in this situation?
Please help!

I was told at a UCAS convention that they usually only consider reconsidering (if that makes sense) when something about your application has changed, you missed something out or you had to clarify on something. So in your case, they'd reconsider. But that doesn't mean you'd 100% get an offer. Just they'll assess your application again