Catching a barrel right after you throw it lets you build up a lot of momentum, in any direction.

If you pick up a barrel, throw it into another one, and quickly pick up both again, you will be holding two barrels at once instead of just one. You can also throw both at the same time.
It also works with three barrels, but it takes a bit of practice to pull it off.

If you aim upwards using the barrel push tech, you can reach a higher position more easily with enough momentum. The best way is to stand on a higher spot, aim the barrel directly below you, and jump. If there’s space underneath, you can throw the barrel down and it will launch you upward from below.