While Quake was generally not designed with the Rocket Jump or Grenade Jump in mind, an exception exists in E4M4: the Palace of Hate where the player must Grenade Jump into a Teleporter to acquire one of the Secrets. A Grenade Jump is similar to a Rocket Jump, but the former is harder to master as the player must time the explosion of the Grenade. However, if correctly done, the player can jump higher or farther than if they were to perform a Rocket Jump.
In Quake II, grenade jumps are possible with both Hand Grenade and Grenade Launcher. After learning what's possible with Quake engine, developers carried this skill just one tick away, just to be included but not limited to their deathmatch maps like Q2DM1: The Edge. Speedrunners can be seen utilizing cooked Hand Grenades until they lay a hand on Rocket Launcher to reach great heights to skip most of the single player map progress without ever needing to stop.
Unless shot at the ground, at beneath own feet straight downward, there's hardly a way to get steady jumps from bouncing Grenade Launcher projectiles solely. Even after possessing most of the arsenal by the end game, Hand Grenades still stay as a great substitute for Grenade Jumps. A well placed Hand Grenade happen to bounce at the point alot less compared to Grenade Launcher projectiles, also can be cooked up for timing the jump and will propel the player up to air higher compared to a Rocket Jump.
Quake III: Arena
Quake III Arena has a different approach at grenade jumps. Like previous installment of the series because of wildly unpredictable jump height of grenade projectiles, Grenade Jumps are highly situational and impractical compared to performing a Rocket Jump. Unless shot at a wall, corner, downstraight, floor beneath or a small pit from a rear angle and certain distance, projectiles don't tend to stand still for a consistent outcome.
However, in a more practical usage; player can trigger Grenade Launcher projectiles together before arming time by shooting a Rocket Launcher at them. Resulted chain explosions will give player a longer air time and capabilities of reaching greater heights.
Despite Quake Live being throughly similar to Q3A, in Quake Live grenade projectiles can't be detonated off within' Rocket Launcher blasts. Yet, it seems like Grenades have a slight deviation that prevents them from vertically locked in a position. Any Grenade projectile shot straight downward tend to slightly move forward instead of bouncing at the spot until detonation.
Grenade jump mechanisms in Quake 4 pretty much similar to the previous installments of the game. Grenade Launcher projectiles best utilized by shooting the floor beneath downstraight to reach the height desired and more control over their blast timer.