Most (if not all) the meters I have do fixed range ohms measurements (typically up to its maximum number of counts) while in continuity mode: Keysight U1282A, U1273A, Samwa PM300 (Dave sells it in his store), Uni-T UT136C/UT61E/UT139C, Brymen BM857, etc. This is done without loss of the beep speed, but obviously the actual measurement is a bit slower. Also, the beep threshold varies a lot, with some limiting this to 20Ω and others to 50Ω.