You can get more Hope points by putting your hopes in danger, but Destiny isn't tied to anything like that, so how do you get more Destiny points? So glad you asked.
You invoke a moment of destiny.
These are those big scenes where everything's come to a head and the music either swells or cuts off dead, and there's probably a slow motion shot somewhere in the immediately future. In short, it's a BIG deal. In this moment, you can accomplish the stuff of legend, but you may exceed a greatness that can be contained in a mortal frame. In short, your glory may cost you your life.
When you invoke a moment of destiny, you double your Destiny rating. The whole thing in one chunk. There's no breaking it up like you do when endangering your hopes. With this, you invoke your moment and every Destiny point in your Pool becomes two. Just think about how much effort you'll be generating with that. You'll probably be running around doing three and four things in an exchange, and still racking up big effort scores.
I've already hinted at the price for this. In almost any epic film or story worth looking at (epic in the classical dramatic sense, not the used-until-meaningless Hollywood epic) the protagonist makes his great play, and then dies. It's not always the case, but it's pretty damn common. Thus, invoking your moment of destiny makes you very fragile. You'll kick ass all over the place, until someone actually manages to touch you.
That's probably when we go to slow mo and cue up Adagio for Strings. But hey, if you did it right, your death doesn't mean anything in terms of the cause anymore. You accomplished a major milestone, maybe even completed what you needed to do and set everything right. You're a hero who will live in legend forever and people will invoke your name for generations. That little house on the hill with the pretty girl and faithful dog though? Not so much.