When one of these plants loses its growth point (to bugs, to herbivores, to my knife) it is quite likely to branch. Here is an example of one of the white finger types after its two growth points were wiped out by mealy bugs.
And here is a picture from habitat showing what looks like the same thing. These plants are tasty to all manner of mammals here (probably for the water, and probably because they lack spines).
Some pictures here to illustrate the coring process, which is how I forced branching on a plant which would not do so otherwise... this is a propagation trick to make more plants from cuttings, when they might not be easily available from seed.
I started by removing the growth point from the center of my biggest plant in January 2015.
Its immediate response was to flower from every available pore (second pic). I removed those inflorescences ASAP and then the head grew back. So then I realized I had to dig deeper, and I gouged another half inch deeper into the center. You would be surprised how deep down the actual core of the plant is in the main stem.
What resulted was a crazy explosion of new heads, some of which were squeezed out, a couple maybe lost to mealy bugs. In the end the four heads in the last picture survived.
As a technical matter, it's probably a good idea to point out that coring one of these plants tends to leave a cavity in the center, which presents a serious risk of rot whenever it might be filled by water. Since these plants are winter growers I did the coring then, which meant I had to move the plant under cover (or move some cover to the plant) during our winter rains. Otherwise I am fairly sure it would have perished. Once it's healed and the new heads are big enough to squeeze together, the risk goes way down.
I am very curious to see your Dudleya pictures. The northern plants are pretty, especially when they flower.