Split multiplexes are throws that deliver balls to more than one hand. (Except in passing situations, this means balls are thrown from a single hand to both hands.) Balls can be thrown to the same height or different heights.
Grouped multiplexes are throws that deliver all balls to a single hand. Both same-hand grouped throws and crossing grouped throws are possible. In either case, balls can be thrown to the same height or different heights. When thrown to the same height, however, this multiplex is difficult to catch, so most common is the differing height, or stacked, multiplex. (Other sources simply make a distinction between split and stacked multiplexes, but I prefer grouped as the general term and stacked as a specific subcategory.)
You generally build up to a multiplex pattern the same way you learned to juggle 3 balls--first with one throw, then with a 2-throw exchange. Exercises helping to integrate these throws into a regular juggling pattern are noted after some descriptions (as To practice:).
Split, same height (2 balls): To throw the balls at the same
height, hold them (with your palm facing upward) in a horizontal line
perpendicular to your forearm. Throw with a normal cascade motion from
the center of your body. Think about your hand moving between the balls,
splitting them apart. It also helps to physically separate the balls in
your hand prior to the throw.
. . . To practice: Just for fun, try throwing a single ball
straight up the middle and then throwing the multiplex underneath so that
the two balls split around it. An easy basic move would be to use this
throw to start a columns pattern.
Stacked, same hand (2 balls): "Stacked" is the equivalent of
"grouped, different heights" as defined above. With your palm up, hold
the balls in line with your forearm (the opposite of the split set-up).
Throw basically straight up (the equivalent of a fountain motion).
. . . To practice: Try doing 3 in one hand, with 2 of the balls in
a stacked multiplex. (2-up, 1-up, 2-up, 1-up.)
Stacked, crossing (2 balls): This should be a natural outgrowth of
the previous trick. Simply throw with a cascade motion rather than
straight up.
. . . To practice: As you practice a two-throw exchange, make sure
you are throwing under the previous throw each time. Try a basic
3-ball cascade with the 2-ball stack replacing one of the normal ball
positions. This is probably the easiest continuous pattern to mentally
latch onto.
. . . Also try this trick with a reverse cascade (over the top) throw.
This is slightly trickier, and leads on to the next trick . . .
Split, different heights (2 balls): You may have noticed when you throw the stacked reverse-cascade throw above that one ball travelled further than the other. Again, you can accentuate this difference by flicking your wrist; in this way you should be able to throw a higher throw across and a lower toss back to the throwing hand. It is important to throw this like a reverse cascade--from the outside, thrown over the top--with a flick of the wrist. Although this may be the most difficult of the basic throws with two balls, it is the easiest way (IMHO) to do a basic five-ball multiplex pattern.
Grouped, same height (2 or more balls): The multiplex catch is the hard part here. Try to keep the balls perfectly together as you throw; start low and use all arm/no hand motion.
Basic 3-ball throw: This is the building block for
the standard 7-ball multiplex pattern. Two balls return to the throwing
hand and one crosses (it qualifies as both grouped and split). I
throw this trick like the split/dif. heights multiplex with two--as a
reverse cascade throw, though other variations may be possible.
. . . To practice: Work toward the seven-ball multiplex pattern
using 4 balls for what would be the 2-ball exchange in learning the
3-ball cascade. Practice throwing the 3-ball group before the single
ball, and then the reverse. When you can get a solid exchange, use five
balls. Throw a single ball from the hand with two and then the 3-ball
multiplex from the other. One hand will be doing the 7-ball multiplex and
the other a 3-ball cascade. Switch hands. When both hands can do this
5-ball pattern, try 7.
3-ball start: A single multiplex throw is a flashy way to start a 3-ball juggle. You could split the balls any way you wish. I usually use a triangle with two high, one low. To do this, arrange the balls with one in your palm and two on the fingers. Throw with a hard flick of the wrist to separate the balls as much as possible. Grab the lower ball with a claw, or bat it back up as it comes down so that you will have time to catch the other two and go into a cascade. You can perform the opposite throw--two low and one high--by placing two balls in your palm and one on your fingers. You can add some glitz to the 3-ball start by throwing behind your back, under your leg, etc.
4-ball start: Identical to the 3-ball start, except with 2 balls in the palm and two on the fingers. If you can't go right into the fountain at first, try going into a multiplex pattern.
5-ball start: Place all five balls flat in your hand, with four in your palm (well, close to your palm) and one forming the peak of the "house" shape on your fingertips. I can do this into the standard multiplex pattern, but would like to see it done into a cascade!