In Ext Designer you can only set multiSelect on the view of a tree and not on the tree itself. This seems the correct way (see documentation of the view), but the resulting tree doesn't allow multiSelect.
If I manually add multiSelect to the treepanel it works, but this is overwritten by every export with Ext Designer.
I'm not sure if this is a bug in Ext Designer or ExtJS 4 itself, because the designer works the way the documentation says. But this doesn't work in the browser.

Using Ext Designer 1.2.2 and ExtJS 4.0.7

A workaround is:
Ext.Function.interceptBefore(Ext.tree.TreePanel.prototype, 'initComponent', function() {
    if ( Ext.isDefined(this.viewConfig.multiSelect) && this.viewConfig.multiSelect )
        this.multiSelect = true;