Here are the rules about jumping:
Your Strength determines how far you can jump.
Long Jump. When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.
High Jump. When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.
Here are the rules about moving a grappled creature:
When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.
What I don't know is whether your maximum long/high jumping distance is also halved by grappling. For example, would someone with a Strength score of 20 (granting a normal maximum running high jump of 8 feet) be able to jump 8 feet up with a grappled creature, or would he only be able to jump 4 feet up?
This assumes the 20 Strength grappler/jumper has made the running start beforehand and has enough total speed, even if halved due to grappling, to make the maneuver.
