There are at least three factors that affect the thickness of your plied yarn.
First, if you want a thicker plied yarn, you can increase the number of plies. The picture here shows exactly the same single (spun from CVM top) in, from bottom to top: a balanced 2-ply, balanced 3-ply, balanced 4-ply and balanced 5-ply.
If you look closely, you'll notice that the 3-ply seems almost as tight as the 2-ply. In part, that's because a balanced 3-ply from the same single as a 2-ply will end up with a steeper twist angle, i.e., it's more tightly ply-twisted, so it squeezes in the singles a bit more. If I were actually spinning for a 3-ply, then, I might use less twist, so my 3-ply twist angle would be similar to my 2-ply's twist angle, and thus get a thicker 3-ply yarn (see method 2).
In general, the more plies, the thicker your plied yarn. How do you ply more than 2 strands? For 3 strands, you can run each one between the fingers of your hand to control them (4 fingers = 3 gaps). For more, it's a bit more of a wrangling session, but you can run two strands through finger-gaps so you have 4 or 5 running up (or more!) and then use the other hand to keep them plying together.
But, really, who wants to keep adding plies? I would hazard to guess that you want a thicker plied yarn, and you don't want to take even longer to get to it than your default two- or three-plying.
So, let's move on to the second way to get a thicker yarn. This one is interesting to contemplate (and do! but more on that in a second). See the picture?
What I did here was put less twist in the thicker yarn. Both singles have exactly the same amount of fiber drafted into the yarn as twist enters. In both, but more closely monitored in the thicker one, I'm spinning without squeezing the yarn -- a "modified woolen" technique (since to be pure woolen, I'd need to be using roving and potentially actually doing real long draw ... u-huh. I wanted to make this do-able!)
So, I'm doing two things here to get the 2-ply thicker: spinning woolen-style, i.e., not squeezing the newly spun yarn just pinching to draft fiber from the combed top, then releasing to let twist up, and re-pinching to draft more out. And I'm putting in less twist.
How do you put in less twist? On a wheel ... treadle slower, or move to a larger flyer whorl (or both!). On a spindle ... twist your spindle at a thicker part of the shaft, or rotate it more slowly (if you thigh roll, try a finger-flick, which is usually slower).
Up to now, I've always drafted the same amount out ... my "default draft" if you like. However, the most obvious way to get a thicker plied yarn might be this third technique: draft more fiber into your yarn.
The picture shows the balanced-two plies resulting from having thicker singles. At the bottom is the default size from before, and moving up each one, I've drafted out more roving (thicker drafting triangle) for the twist to move into so that the singles are thicker.
How do you draft out more fiber? I've noticed that many, many spinners have a default amount of fiber they draft. When I teach people to spin thicker yarns, I start by handing them pencil roving and have them spin without drafting at all. Almost everyone stumbles at this ... they automatically fall into drafting by default! But with focus and practice, they can control their hands and stop the drafting.
This is an extreme, however -- once you can spin without drafting, then you can attempt to spin while drafting less -- leaving more fiber in your drafting triangle to become yarn.
With a wheel, you can also change its settings to help your automatic drafting contain more yarn in the drafting triangle: increase draw-in by increasing the tension on the drive band, and for scotch-tension or irish-tension wheels, increase the tension on the brake band as well. This will make the fiber move out of your hand more quickly, giving you less time to draft.
Moving to a larger whorl also helps you draft out more fiber in a larger drafting triangle, since to make yarn at a slower speed, you need a wider diameter yarn.
On a spindle, use a heavier spindle and spin it more slowly to encourage a larger drafting triangle.
Whew! Got all that?
I'd love to hear if you try any of these, and how they work for you. We so often think about spinning thicker singles, but seldom consider how to spin thicker plied yarns. If there's something you do to spin thicker plied yarns, I'd love to hear so I can try it too!
Thanks, and happy spinning!