Currently the RadTileView doesn't support this behavior, but you can achieve something similar with two RadTileViews - one will contain the "minimized item" and the other one will contain only the maximized one.
In the PreviewTileStateChanged EventHandler you can see the new maximized item, handle the event (so that the item won't maximize) and add this item to the other RadTileView.
For further references could you please examine the attached project and see if this is what you're looking for?
p.s. There's a small bug in the RadTileViewItem when you handle the PreviewTileStateChanged event, but I've provided a workaround for it in the attached project.
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