Customizing a modal presentation of a view controller would be tricky before iOS 7. It got much easier with the addition of the transitioningDelegate protocol. This delegate would be able to vend an animation controller and an interaction controller for presentation and dismissal on the view controller which implemented them.
Without that, if you wanted a “burger menu” then you had to implement a custom container controller like I did with DTSidePanel in DTFoundation 1.4, three years ago. Things have gotten much easier a year ago.
A client of ours liked the way the Linked In app showed related apps in a modal side panel and so I went to research how you would that most reusably nowadays.