Change map type on tiles view?

I'm really enjoying the Tiles view, and filling in all the gaps is a fun challenge. But there are some where the default map on the website makes it a bit tricky to see how I'd get there, and it would be great to be able to switch the map to one of the other views (OSM/de/CyclOSM) like I can on the main /map. Any chance that switcher could be turned on for the tiles map too?