Renaissance recorders vary in range. My Mollenhauer Kynseker G alto goes well into the third octave, and Ganassi's "La Fontegara" (the first recorder tutor ever written) has fingerings up there - you can get reproductions pf Ganassi recorders, though they're very expensive. But I've tried a Kynseker bass that could only do an octave and a fifth (albeit at shattering volume).

Any recently made renaissance-type recorder from tenor up should be able to do two octaves.