Blue Origin says the BE-3PM engine in its New Shepard vehicle can throttle down to 18% max thrust.
Compare to 57% for the Merlin 1D engine in stage 1 of SpaceX's Falcon 9 (and to 39% for the Merlin ...
At launch, a vehicle like the space shuttle would command its throttle to do a few things:
Ramp up to max throttle
Hold max throttle
Follow a throttle bucket as function of velocity when near max-Q