you can catch the orientation changes by overriding the method willTransitionToTraitCollection:withTransitionCoordinator
: in view controller, and then can update the constraints accordingly. And yes as you have mentioned if you need to change multiplier then you will first have to remove the constraint and then apply it again. If you know at compile time what multiplier you would be using in both orientations then i would suggest to use interface builder to create separate constraints with different multipliers for distinct size classes.
Useful Material
Adaptive and Size Changes Reference