Make Tile.DisplayIndex property a dependency property so it can be can be set through data binding.
Create a feature in the RadTileList control that allows the user to select multiple tiles, but only one (or maybe, any number - it could be a property that is set for this specific kind of selection) per group.
This was first discussed on this forum thread: https://www.telerik.com/forums/multiple-selection-single-selection-per-group and it's the reason behind this feature request.
The current workaround to overcome this "issue" is also available through that link.
Please provide an event for when a Tile gets moved and/or when a Tile gets placed into a group or removed from a group. Something simple like OnTileMoved with event args pointing to the tile and new values (like updated group) would be peachy. :)
This will allow to have different visual customization for the separate groups.