Recorder music is usually written within a range of two octaves and a tone. Some music demands higher notes, and some instruments can obtain these higher notes. Two and a half is certainly possible, although the fingerings are somewhat awkward and they're quite difficult to play in tune.
Three octaves? I don't think I've ever heard of a recorder capable of three octaves. There are some physical conflicts between it being a recorder (and sounding like one) and having that kind of range capability.
One reason is because of the windway, which limits access to higher overblown registers which you can access on a transverse flute by modifying your embrochure. It's harder to play in the first place, but has more capability once you've mastered it.
You're not going to find something that actually has the same fingering as a recorder - fingering is fundamentally linked to the physics of the instrument. Recorder fingering is particularly tricky - if you learn a Boehm system woodwind instrument you'll find it's actually a lot simpler, because the keywork takes out some of the cross-fingerings and half-holings that recorder players are so used to.
Yamaha have recently launched a single-reed instrument with recorder fingering - the Venova - but it's not got any more range than a recorder has. Again, physics has got in the way (and they had to do some really weird engineering on it to make it work - it's actually got a split bore!)