How can I expand a MKMapRect by a fixed percentage?

What about converting the visibleMapRect to a CGRect with rectForMapRect:, getting a new CGRect with CGRectInset and then converting it back to a MKMapRect with mapRectForRect:?

In iOS7, rectForMapRect: and mapRectForRect: has been deprecated and now are part of the MKOverlayRenderer class. I'd rather recommend to use the MapView mapRectThatFits: edgePadding: methods. Here is a sample code :

MKMapRect visibleRect = self.mapView.visibleMapRect;
UIEdgeInsets insets = UIEdgeInsetsMake(50, 50, 50, 50);
MKMapRect biggerRect = [self.mapView mapRectThatFits:visibleRect edgePadding:insets];

latest Swift for 2017...

func updateMap() {

    mkMap.removeAnnotations(mkMap.annotations)
    mkMap.addAnnotations(yourAnnotationsArray)

    var union = MKMapRectNull

    for p in yourAnnotationsArray {
        // make a small, say, 50meter square for each
        let pReg = MKCoordinateRegionMakeWithDistance( pa.coordinate, 50, 50 )
        // convert it to a MKMapRect
        let r = mkMapRect(forMKCoordinateRegion: pReg)

        // union all of those
        union = MKMapRectUnion(union, r)

        // probably want to turn on the "sign" for each
        mkMap.selectAnnotation(pa, animated: false)
    }

    // expand the union, using the new #edgePadding call. T,L,B,R
    let f = mkMap.mapRectThatFits(union, edgePadding: UIEdgeInsetsMake(70, 0, 10, 35))

    // NOTE you want the TOP padding much bigger than the BOTTOM padding
    // because the pins/signs are actually very tall

    mkMap.setVisibleMapRect(f, animated: false)

}

Simple and clean solution for Xcode 10+, Swift 4.2

Just set the edge insets for the maps' margins like this:

self.mapView.layoutMargins = UIEdgeInsets(top: 8, right: 8, bottom: 8, left: 8)
self.mapView.showAnnotations(map.annotations, animated: true)

Please let us know if it works for you.